aa r X i v : . [ phy s i c s . h i s t - ph ] M a r Why Do You Think It is a Black Hole?
Galina Weinstein ∗ The Department of Philosophy, University of Haifa, Haifa, theInterdisciplinary Center (IDC), Herzliya, Israel.
March 2, 2021
Abstract
This paper analyzes the experiment presented in 2019 by the EventHorizon Telescope (EHT) Collaboration that unveiled the first image ofthe supermassive black hole at the center of galaxy M87. The very firstquestion asked by the EHT Collaboration was: What is the compactobject at the center of galaxy M87? Does it have a horizon? Is it a Kerrblack hole? In order to answer these questions, the EHT Collaborationfirst endorsed the working hypothesis that the central object is a blackhole described by the Kerr metric, i.e. a spinning Kerr black hole aspredicted by classical general relativity. They chose this hypothesis basedon previous research and observations of the galaxy M87. After havingadopted the Kerr black hole hypothesis, the EHT Collaboration proceededto test it. They confronted this hypothesis with the data collected inthe 2017 EHT experiment. They then compared the Kerr rotating blackhole hypothesis with alternative explanations and finally found that theirhypothesis was consistent with the data. In this paper, I describe thecomplex methods used to test the spinning Kerr black hole hypothesis. Iconclude this paper with a discussion of the implications of the findingspresented here with respect to Hawking radiation.
In April 2019 an international collaboration of scientists (hereafter EHT Col-laboration) unveiled an image that shows an apparently blurred asymmetricring around a dark shadow. After comparison with computer models, the pic-ture was interpreted as showing a supermassive black hole at the center of thegalaxy Messier 87 (hereafter M87). This interpretation fitted well with the-ory and simulation, according to which the M87 black hole is one of the twolargest supermassive black holes on the sky along with the Sagittarius A (here-after Sgr A) black hole (at the center of the Milky Way, near the border of theconstellations Sagittarius and Scorpius). ∗ This work is supported by ERC advanced grant number 834735.
The Astrophysical JournalLetters in April 2019, which contain a complete exposition of the experiment[10]-[15].In section 7, I discuss a paper (letter) submitted at about the same time asthe six EHT [10]-[15] letters. The paper discusses the GW150914 gravitationalwave event. The authors also adopt the Kerr black hole hypothesis and test it.In both cases – the EHT experiment and the gravitational wave experiment –the Kerr black hole hypothesis is selected as the best explanation. I discuss thephilosophical implications of this selection in Section 8. I end this paper withSection 9, discussing the philosophical significance of the findings presented herewith respect to Hawking radiation. 2
Evidence and interpretation of the evidence
In 2000, Heino Falcke et al. performed simulations of an optically thin emittingaccretion disk surrounding a maximally spinning supermassive Kerr black holewith spin a ∗ = 0 .
998 and mass M BH = 2 . × M ⊙ [solar masses ( M ⊙ ), a ∗ is defined by equation (1) in Section 3]. They presented ray traced images andimages seen for a wavelength of 1.3 mm and wrote that “a marked deficit of theobserved intensity inside the apparent boundary” is produced “which we referto as the ‘shadow’ of the black hole”. They further noted that to simulate theimages we need a Very Long Baseline Interferometry (hereafter VLBI) array ofradio telescopes located ≈ , km apart [8], p. L14.Event-horizon observations of the core of the galaxy M87 were conductedon the two consecutive nights of April 5/6, 2017 and again four nights later onthe two consecutive nights of April 10/11, 2017. The observations were madeat a wavelength of 1.3 mm and from a VLBI array of radio telescopes located ≈ , km apart. Scan durations of M87 varied between three and sevenminutes and the quasar 3C 279 was also scanned as a calibrator source. Thecompact object at the center of M87 was observed with eight telescopes at sixgeographic sites and it was the first time that the small array called AtacamaLarge Millimeter/submillimeter Array (hereafter ALMA) has been included inthe VLBI array. This whole array is referred to as the EHT.After Correlation, the visibility V ij data were calibrated by three calibrationpipelines EHT-HOPS , rPICARD and AIPS (Python-based scripts using modulesfrom the EHT analysis toolkit, the eat library). Phase errors (fringe-fitting)and atmospheric (turbulence and variations) errors were corrected and fixed– and the amount of data was consequently reduced so that noisy data wasremoved. All three pipelines produced data – visibility amplitudes as a functionof baseline – with a slight anisotropy. One can see peaks in the observed visibilityamplitudes that appear across all four observed days. These peaks have twominima, nulls, on either side and at the location of the minima the visibilityamplitudes of the data are very low. The first of the nulls occurs at ∼ . Gλ (giga-lambda) and the second is observed at ∼ . Gλ . The high peak betweenthese two nulls is at ∼ Gλ . A single pipeline output, the EHT-HOPS , wasdesignated as the primary data set of the engineering data release [11], p. 14;[12], p. 2, 5-8, pp. 23-24.Residual station-based amplitude and phase calibration errors neverthelesspersist after performing calibration steps and overwhelmingly dominate the re-maining thermal random Gaussian noise ǫ . It is therefore possible to constructdata products that are insensitive to these systematic errors. Such quantities The radio signals collected by each telescope are digitized and labeled with timestampscreated by atomic clocks at each site and then recorded to hard drives. The data are readfrom each hard drive to a correlator and then processed by the correlator’s software, whichmatches up and compares the data streams from every possible pairing of the EHT’s eighttelescopes. After correlation, the complex visibility data V ij are obtained. V ij is the outputof the correlator and the fundamental data product which gives information of both theamplitude and the phase of the fringes of the signal on a baseline (distance between twotelescopes/stations) i and j . In June 2018 the EHT Collaboration split up into four teams in differentregions of the world and each team chose a different imaging method and workedin isolation for seven weeks on the data. The 2017 EHT April 11 data wasselected. The teams neither talked nor crossed photos and that enabled themto avoid getting into collective bias influencing their final images. Each one of thefour teams relied upon the judgment of its members to select a different imagingmethod to convert the data into images: teams 1 and 2 used the RegularizedMaximum Likelihood (hereafter RML) method, while Teams 3 and 4 used aversion of the CLEAN algorithm [13], p. 9. In July, 2018, all four teams came together and revealed for the first timethe four images they had produced. Although not precisely identical, whencomparing images, all four teams obtained an image of a crescent with a centraldark area surrounded by an asymmetric ring. The initial blind imaging stageindicated that the image was dominated by an angular ring diameter (an angularcrescent diameter) of θ d ∼ µas [13], p. 9.The next stage of the experiment required the objective evaluation of thefidelity of the images reconstructed in the first stage. That is, the second stageinvolved selecting imaging parameters that are independent of expert judgment.Three imaging Python pipelines, DIFMAP (Difference Mapping),
SMILI (Sparse At high frequencies, visibility amplitude and phase calibration are made extremely diffi-cult. Amplitude gain ( g i and g j ) and phase (Φ i and Φ j ) errors corrupt the measured visibility: V ij = g i g j V ij e i (Φ i − Φ j ) + ǫ , where V ij stands for the unknown model visibility (the ideal mea-sured visibility with no atmospheric corruption). Radio waves from M87 reach station i beforereaching station j . Closure phase is the product of three visibilities (from three stations). It isformed from baseline visibilities on a closed triangle ijk . Consider three telescopes ijk . Thevisibility we measure on baseline ij is: ( u , v ) ij plus phase error at the station ( i − j ). Themeasured visibility on baseline jk is: ( u , v ) jk plus phase error ( j − k ) and the one measuredon baseline ki is: ( u , v ) ki plus phase error ( k − i ). Now the phase errors ( i − j ) + ( j − k ) +( k − i ) are all canceled when the phase visibilities are added up, leaving a quantity: ( u, v ) ij + ( u, v ) jk + ( u, v ) ki such that the baselines “close”. The logarithmic closure amplitude isconstructed from combinations of visibilities measured on four stations and is insensitive tovariations in the amplitude gains [13], pp. 2-4. The reason for selecting the 2017 EHT April 11 data set was that, on that observingday, the EHT array of radio antennas covered the largest area for M87 and the amplitudecalibration among stations was the most stable. The two imaging techniques used in generating the 2017 EHT black hole images arebased on the traditional deconvolution CLEAN algorithm and the RML method. Imagingalgorithms are broadly categorized into two methodologies: inverse modeling (CLEAN) andforward modeling (RML). 1) CLEAN: The sky is only sparsely sampled by the VLBI array.The original CLEAN algorithm begins with a Fourier transform of the sampled visibilities(the dirty image). The algorithm then proceeds to find the points of highest intensity in thedirty image. The process is iterative and iterations are continued until a desired noise level(a stopping criterion) is achieved in the dirty image. Finally, CLEAN takes the accumulatedpoint source model and convolves the image with a restoring beam, a clean beam, Gaussianbeam of full width at half maximum (FWHM), instead of the dirty beam. The algorithm addsthe residuals of the dirty image to this image to form the CLEAN image. 2) RML is based onmaximum likelihood estimation (MLE): finding the best fit image that minimizes a functionthat is a sum of a chi-squared χ function corresponding to data and another function calledregularizer. Regularization may include smoothness (requiring that the image be smooth) orsparsity) [10], p. 4; [13], p. 4. eht-imaging , have been designed. The SMILI and eht-imaging pipelines are based on RML and
DIFMAP is a CLEAN Pythonscript. The pipelines employ an iterative imaging loop, alternately imagingand self-calibrating the data (visibility amplitudes and closure quantities)[13],p. 12. Four training geometric models of sources with different compact structure(a ring, a crescent, a disk and two blobs) were considered. The models werechosen such that their visibility amplitude data on EHT baselines matchedsalient features of the observations, in particular the first visibility null at at ∼ . Gλ and the second at ∼ . Gλ . You might rightly think that a disk candefinitely not fit the 2017 EHT data. But all four models produce images ofobjects having an apparent diameter of ≈ µas . Further, all of the geometriccompact objects have a total flux density of 0 . . MeqSilhouette and eht-imaging . While
MeqSilhouette was used for comparison, eht-imaging ’s synthetic data were used for image-reconstruction.Each one of the three pipelines,
DIFMAP , eht-imaging and SMILI , has fixedsettings (such as the pixel size) and also parameters taken as arguments. Thoseimaging parameter combinations for the three different imaging pipelines werederived by conducting parameter space surveys on synthetic data. To determinea single combination of the best performing hyper parameters for each pipeline,called fiducial parameters, many similar-looking images were reconstructed fromthe synthetic data (produced by eht-imaging ).The images were reconstructed using 50 ,
000 possible parameter combina-tions, which also included values that were expected to produce poor recon-structions. The images were then compared with images that were generated DIFMAP is a CLEAN Python script implemented in DIFMAP, a software package originallywritten by Martin Shepherd in the 1990s. After loops of cleaning and self-calibration, the
DIFMAP script generates final cleaned images. The
SMILI and eht-imaging pipelines havebeen developed by the EHT Collaboration. The
SMILI
Python-interfaced library is basedon sparse sampling, reconstruction of images from sparse data. NumPy and SciPy powerthe main tasks of eht-imaging and the main imaging methods are powered by the routine scipy.optimize.minimize . Other libraries used in creating the 2017 EHT image are: Astropy,Pandas, and Matplotlib by which the black hole image is visualized and processed. The eht-imaging pipeline handles self-calibration by minimizing: χ = P i SMILI both have seven parameters as argu-ments: the total flux density; the fractional systematic error on the measured visibilities, theFWHM of the circular Gaussian initial image, and four regularization terms. Reconstructed images of data sets from observations made onApril 5, 6, and 10 were subsequently incorporated, while preventing the poorestreconstructions of 2017 EHT April 10 from dominating the outcome. The bestfiducial 2017 EHT images, for each of the four observed days, from each of thethree imaging pipelines, were subsequently selected, the averages of which weretaken and restored to an equivalent resolution of the EHT array. The imagesproduced from the three pipelines are broadly consistent across all four observingdays and show a central shadow and a prominent asymmetric ring having anenhanced brightness toward the south. The EHT Collaboration formed a singleimage, which they called the consensus image , from the average of each day.This image is the famous black hole image of M87 [10], p. 5; [13], pp. 7-21, p.22, pp. 32-33, pp. 37-41; [15], p. 46; [33], p. pp. 5-6.Having reconstructed images by DIFMAP , SMILI and eht-imaging , validationtests were performed to assess their reliability. Recall that in April 2017, obser-vations of the calibrator 3C 279 were performed with the EHT. Images of 3C A Python module ehtplot with a color submodule has been created, a perceptually uni-form colourmap that is used in the reconstruction and simulations of images. The colors ofthe images represent the brightness temperature which does not necessarily correspond to anyphysical temperature of the radio emitting plasma in the jets and accretion disk [13], pp. 8-9. 679 were reconstructed and self-calibrated by DIFMAP , SMILI and eht-imaging and then compared with the 2017 EHT M87 images. It was shown that stationgains in both cases were broadly consistent. It was then concluded that consis-tency between the two sources M87 and 3C279 and among the three differentpipelines provides confidence that the gain corrections are not imaging artifactsor missing structures in the 2017 EHT images [13], pp. 22-24.Finally, reconstructed images were generated using SMILI , eht-imaging and DIFMAP , the purpose of which was to extract θ d . θ d was extracted in the imagedomain of the fiducial images, for each of the four observed days, from eachimaging pipeline ( SMILI , eht-imaging and DIFMAP ). The images were gener-ated with the fiducial hyper-parameters. Unlike the SMILI and eht-imaging images, the ones obtained by DIFMAP were restored with a FWHM Gaussian20 µas beam. The measured image domain ring diameters θ d were nonethelessconsistent among all imaging pipelines. Across all days, the DIFMAP images re-covered an average value of θ d ≈ ± µas when restored with a 20 µas . The SMILI and eht-imaging images recovered an average value of θ d ≈ ± µas .It is written at the end of the fourth letter: “These first images from the EHTachieve the highest angular resolution in the history of ground-based VLBI”[13], pp. 29-31. This is certainly true. The 2017 EHT data were subsequentlyinterpreted. In the fifth letter, the EHT Collaboration is endorsing the hypothesis that atthe center of M87 there is a supermassive Kerr rotating black hole [14], p.1. The Kerr solution of the Einstein field equations describes the spacetimegeometry around astrophysical rotating black holes. An alternative hypothesisfor what could be the compact object at the center of M87 had been checkedand discarded before the 2017 EHT experiment was performed. This alternativeis the hypothesis that the compact object at the center of M87 has no horizonbut has a surface (such compact object could be very dense neutron stars andsupermassive stars).In 2015 a team of scientists belonging to the EHT Collaboration made anexperiment the goal of which was to compare the merits of the two rival hy-potheses: a compact object with a surface and a black hole with a horizon; andthen choose which hypothesis can best explain the evidence. At the time inwhich the experiment was conducted, the EHT consisted of only three stations(radio telescopes). Were a compact object with a surface present at the center ofM87 instead of a black hole with a horizon, said the team, its photosphere wouldbe heated by the constant deposition of kinetic energy from the accretion gas.In the absence of an event horizon, the photosphere would therefore radiate,resulting in an additional component in the measured spectrum. The surfaceluminosity is proportional to the average mass accretion rate on the surface.The implication is that if the object at the center of M87 has a horizon, thekinetic energy of the accreting gas must advect past an event horizon, beyond7hich it is no longer visible to distant observers. In simple terms, a compactobject with a surface would appear brighter than a black hole with a horizon.It was found that the existence of an observable photosphere in the core of M87was ruled out. “The implication is that the kinetic energy of the gas is advectedpast an event horizon, beyond which it is no longer visible to distant observers.In other words, M87* must have an event horizon” [5], pp. 7-8, and the blackhole hypothesis was selected.In the fifth letter, it is written: “In this Letter we adopt the working hypoth-esis that the central object is a black hole described by the Kerr metric, withmass M and dimensionless spin a ∗ ”. After having adopted the Kerr metric andthe no-hair theorem, the EHT Collaboration proceeds to test the Kerr metricby fitting GRMHD models to 2017 EHT data. A GRMHD Simulation Library has been generated from several differentcodes. Forty-three high-resolution, three-dimensional Standard and NormalEvolution (SANE) and Magnetically Arrested Disk (MAD) simulations, coveringwell the physical properties of magnetized accretion flows onto Kerr black holes,were performed by varying two dimensionless parameters:1) The spin a ∗ : a ∗ ≡ JcGM BH , − < a ∗ < . (1)where G is the universal gravitational constant, c is the velocity of light.If G = c = 1, then: a ∗ ≈ JM BH .2) The magnetic flux φ : The Kerr metric was proved to be the unique stationary, asymptotically flat, vacuumsolution with an event horizon. It was shown that the Kerr-Newman solution involves justthree free parameters: mass M BH , angular momentum J (spin a ∗ ) and charge Q . This isthe no-hair theorem which states that non-charged black holes are uniquely characterized bytheir mass M BH and angular momentum J and are described by the Kerr metric. The blackhole is governed by general relativity (GR). Magnetohydrodynamics (MHD) is the frameworkthat governs the dynamics of the accretion flow and jets around the black hole. The plasmais treated as a fluid and numerical methods to integrate the GRMHD equations are searchedfor. 1) The Black Hole Accretion Code (BHAC) performs magnetohydrodynamical simulationsof an accretion flow onto a black hole. The ions (protons) and the electrons in the accretiondisk plasma travel quite a long distance along magnetic field lines before being scattered. Thisand other factors complicate the calculations and require more computational power. 2) Asystem called H-AMR (Hierarchical Adaptive Mesh Refinement) is used, which acceleratesGRMHD calculations by implementing the AMR strategy: a method that reduces the num-ber of computations. 3) Two additional codes, a 3D version of High Accuracy RelativisticMagnetohydrodynamics (iharm3D) and 4) KORAL [Kod radiacyjny L (in Polish)], solve theGRMHD conservation laws by a shock-capturing method [27], pp. 6–8, p. 31. The SANE and MAD models are an approximation of the complex non-linear generalrelativistic dynamical system of a magnetized accretion disk flow orbiting a rotating super-massive black hole. Models with φ ≈ φ ≈ 15, the large-scale magnetic field accumulated by the accretiondisk stops the accretion flow. Models with φ ≈ 15 are conventionally referred to as MAD. = Φ BH q ˙ M R g c , ≤ φ < . (2)where Φ BH is the magnetic flux, ˙ M is the mass accretion rate (the rate at whichmass is accreted onto a black hole) and R g is the gravitational radius definedby equation (4) below.The Simulation Library contains SANE models with a ∗ = − . − . 5, 0,0 . 5, 0 . 75, 0 . 88, 0 . 94, 0 . 97, and 0 . 98, and MAD models with a ∗ = − . − . . 5, 0 . 75, and 0 . r + = R g (cid:16) p − a ∗ (cid:17) . (3)where R g is given by: R g = GM BH c . (4)In order to produce images from the simulations, the following parameterswere fixed in the GRMHD simulations:1) PA . The position angle of the forward radio jet measured east of north.Based on prior knowledge from observations, the chosen value was: P A ≈ .2) i . The observer inclination, the orientation of the observer through P A .Based on prior knowledge from observations, images were generated at i = 12 ,17 , 22 , 158 , 163 , and 168 and a few at i = 148 . Basically, images weregenerated at two major inclinations 17 and 163 .3) θ g . The image scale: θ g = GM BH dc . (5)If G = c = 1, then θ g ≈ M BH d , where d is the distance to M87: d = 16 . ± . θ g represents the angular gravitational radius.For M BH “we use the most likely value from the stellar absorption-line work, M BH ≈ . × M ⊙ ([16]), see explanation in Section 5].Inserting the above value of M BH into equation (9) from Section 5: θ d = . M BH d ≈ . µas is calculated.4) F ν . The total compact flux density measured in Jy (Jansky). The averageflux density of 1 . mm (230GHz) emission is 0 . At φ > ≈ 15, numerical simulations show that the accumulated magnetic flux erupts, pushesaside the accretion flow, and escapes [14], p. 4. R high . The temperature ratio of electrons to protons. Images weregenerated at: R high = 1, 10, 20, 40, 80, and 160.After fixing the values of these parameters ( M BH d , i , P A , F ν , R high ) snap-shots were drawn from the time evolution of the simulation at a cadence ofevery: 10 − R g c .From the SANE and MAD simulations, more than 60,000 synthetic 1 . mm snapshot images were produced by three general relativistic ray-tracing (GRRT)codes, ipole , RAPTOR and BHOSS . The snapshot images created by GRRT codesshow the black hole with a variety of accretion flows and jets and depict a yellow-orange asymmetric bright ring around a central dark shadow (a crescent).Each snapshot image generates a single snapshot model (SSM) defined bythree parameters: F ν , θ g , P A . The snapshot images were compared with the2017 EHT April 6 data set. Comparison of models to data was performed by computing the distance χ ν between the data and the snapshot image. In the course of computing χ ν , thethree parameters F ν , θ g , P A and the gains g i at each VLBI station are varied“in order to give each image every opportunity to fit the data” [14], p. 8.Variations in the three parameters F ν , θ g , P A approximately correspond tovariations in the accretion rate, black hole mass, and orientation of the blackhole spin, respectively. In fitting GRMHD snapshot images to data, the imageis stretched by adjusting θ g (cid:0) M BH D (cid:1) , re-scaled by varying F ν and rotated bychanging P A . Varying the parameters a ∗ , φ and R high can change the widthand asymmetry of the photon ring and introduce additional structures exteriorand interior to the photon ring [14], pp. 7-8.Fitting models to data was performed by two different methods: GENA (agenetic algorithm) . And THEMIS , a Bayesian parameter estimation and model The plasma in the accretion disk is an accretion flow which is composed of ions andelectrons. Both species have the same temperature in the funnel (the strongly magnetizedregions of the accretion flow), but have a substantially different temperature in the middleof the accretion disk (the weakly magnetized regions). Assuming the gas is composed of nonrelativistic ions with temperature T i and relativistic electrons with temperature T e , the ratioof the temperatures of the two species can be imposed in terms of a single parameter R high .Relativistic electrons emit radio photons at 1 . mm wavelength observed by the EHT knownas synchrotron radiation. If the synchrotron radiation is emitted from weakly magnetizedregions: T i ≈ T e . If the emission comes from the funnel: T i T e ≈ R high [14], pp. 4-5, p. 12. Model-fitting requires a large number of scans. The number of scans obtained of M87’scompact object each night ranged from seven on April 10 to twenty-five on April 6. The reduced chi-squared statistic χ ν . χ ν ≡ χν ≡ χN − M , where ν represents the degreesof freedom, N is the number of data values and M is the number of free parameters. GENA fits models to data by finding the model parameters which minimize a χ ν statistic.It implements the differential evolution (DE) algorithm, an optimization algorithm inspiredby natural evolution theory. The major steps of DE are the following: A random populationof model parameters (individuals, parents) is created. Fitness of parameters with the data(visibility amplitudes and closure phases) is computed. Fitness is inversely proportional to THEMIS uses a Differential Evolution Markov Chain Monte Carlo(DE-MCMC) sampler to produce Bayesian posterior estimates for the threeparameters F ν , θ g , P A whilst GENA uses a DE algorithm for producing best fitestimates for the three parameters [4], p. 4; pp. 15-16; [10], pp. 3-6, p. 10, p.36; [13], pp. 8-9, p. 14, p. 28; [14], p. 3, pp. 7-8; [15], p. 6, p. 15.Computing the distance χ ν between the data and the snapshot images is adifficult challenge. That is because of stochastic fluctuations, associated withturbulence in the underlying accretion flow in the GRMHD simulations thatproduce large variations in image structure. On the other hand, data prod-ucts are calibrated and self-calibrated. There is, therefore, dominance of thestochastic image features over the observational noise. This implies that indi-vidual snapshots are highly unlikely to provide an acceptable fit with χ ν ≈ THEMIS Average ImageScoring (AIS). That is, models are rejected if none of the snapshots are as sim-ilar to the average image as the data. In the sixth letter it is noted that “the‘true’ model is necessarily accepted by the THEMIS -AIS procedure” [15], p. 34.That is, the model that would fit the evidence would be the “true” model.It is shown in the fifth letter that the distribution of M Bh d from fitting snap-shot images to data using THEMIS and GENA gives qualitatively similar results. χ ν . The fitness of F ν , θ g , P A with the data is computed such that maximizing fitness ofparameters to data minimizes the value of χ ν . In genetic algorithms, based on their fitness,best-fit parameters (parents) are improved (selected) by iterations in which mutation is used. GENA , however, utilizes a Nondominated Sorting GA (NSGA) , the NSGA-II , to explore theparameter space. NSGA implements an elitist selection process for multi-objective optimization.A population of parents is generated randomly. Offsprings are compared with parents. If theoffsprings do not dominate their parents, they are sorted, moved to the next generation andthe parents are replaced. If the offsprings dominate their parents, they are not elite offspringsand are rejected. The process of selecting the non-dominated offsprings continues until theinitial population of parents is replaced. GENA further uses the procedure of network amplitudecalibration of the residual station gains g i , g j performed by the eht-imaging pipeline. THEMIS uses the (differential evolution) DE-MCMC (Markov chain Monte Carlo) samplerin which many chains are run in parallel. An MCMC sampler is a random walk methodthrough parameter space for performing Bayesian inference. It randomly samples the pos-terior probability distribution of parameters and generates a sequence of random samples ofparameters that fits the data. The parameter is dependent upon the previous one in the chain.DE-MCMC is especially efficient in sampling from models with highly correlated parameters. THEMIS implements a parallel-tempering algorithm for DE-MCMC. Parallel tempering is amethod based on an analogy with statistical physics, called thermodynamic integration, tocalculate the Bayesian evidence. Many MCMC chains are run in parallel on tempered versionsof the original likelihood function at different temperatures. Within THEMIS at each MCMCstep, the station gains g i , g j are addressed by marginalizing over the nuisance parameters.Gain amplitudes g i represent approximately between 40 and 143 additional nuisance parame-ters per data set. The gain parameters are subsumed into the likelihood and incorporated asmodel parameters. Assuming Gaussian priors, the log-likelihood: L = − P i 11s better fits are required, the distribution of M Bh d from fitting snapshot imagesto 2017 EHT data narrows and peaks close to M Bh d ≈ . µas . So, most modelsfavor M Bh d ≈ . µas . The exception is the a ∗ = − . 94 and R high = 1 SANEmodel which favors a small M Bh d ≈ µas [14], p. 10.The best fit P A were then searched for. Recall that P A approximatelycorresponds to the orientation of the black hole spin a ∗ . The SANE and MADsnapshot images were divided into two groups: the spin-away models and thespin-toward models . In each group, the accretion flow either moves with theblack hole’s spin or against it (prograde and retrograde, respectively). The values of the large-scale jet P A were found by the fitting procedure( THEMIS and GENA ) to be 150 -200 east to north, consistent with the spin-awaymodels and inconsistent with the spin toward models. The two chosen cases –prograde ( i = 163 and a ∗ > 0) and retrograde ( i = 17 and a ∗ < 0) – weretherefore the spin-away models, the ones in which the spin of the black hole a ∗ must always be moving clockwise (as seen from Earth) and the bright sectionis at the bottom part of the ring. This means there is a persistent asymmetrywith the brightest region to the South [14], p. 8, p. 10.It was found that the large-scale jet P A lies on the shoulder of the spin-awaymodels but lies off the shoulder of the spin-toward models. The conclusion was:the alternative GRMHD model images having a bright section of the ring at thetop – the spin-toward models, a ∗ is moving anticlockwise (as seen from Earth)– do not represent observations. The snapshot images with the bright section ofthe ring at the bottom capture the qualitative features found in the 2017 EHT2017 April 6 image.It is explained in the fifth letter that the ring is brighter at the bottombecause the plasma is moving toward us. Due to Doppler beaming, at the top,the ring is less bright because the material is moving away from us. Whilethe approaching side of the plasma of the forward jet is Doppler boosted, thereceding side is Doppler dimmed, producing a surface brightness contrast [14],p. 3.The above finding implies that the sense of rotation of both the jet and thefunnel wall (the strongly magnetized region of the accretion flow) are controlledby the black hole spin a ∗ [14], p. 8. This was a hint that the Blandford-Znajekprocess may be confirmed here [2]. More on this below.After performing the AIS test, only very few models were rejected. In thefifth letter it is said that “the majority of the simulation library models isconsistent with the data” and it is then explained that “Given the uncertaintiesin the model – and our lack of knowledge of the source prior to EHT2017 – it In which the black hole’s spin a ∗ points away from Earth ( i > , and a ∗ > 0, or i < and a ∗ < In which the black hole’s spin a ∗ points toward Earth ( i > , and a ∗ < 0, or i < and a ∗ > If the accretion flow’s angular momentum and that of the black hole J are aligned, theaccretion disk is prograde ( a ∗ ≥ 0) with respect to the black hole spin axis. But if theblack hole’s angular momentum J is opposite that of the accretion flow, the accretion disk isretrograde ( a ∗ < 12s remarkable that so many of the models are acceptable” [14], pp. 5-15, p. 19;[15], p. 10, pp. 14-15, pp. 30-33; [4], p. 4.What that meant was that the majority of the models were “true” models.The ensuing steps therefore required narrowing down the range of the best-fit models by imposing three constraints, the most important of which wasthe jet power constraint. Based on measurements performed in 2012, 2015and 2016, the jet power P jet of the core of M87 was assumed to be large: P jet > ergs − . The jet power constraint rejected the largest number ofmodels.Although in the GRMHD models, “the most likely value from the stellarabsorption-line work M BH ≈ . × M ⊙ ” was used, for some GRMHD models,images were also generated with M BH ≈ . × M ⊙ “to check that the analysisresults are not predetermined by the input black hole mass” [14], p. 5.For a given magnetic field configuration: P jet = ˙ Mc . It was found by THEMIS -AIS that the SANE model with a ∗ − . 94 and R high = 1 and with M BH ≈ . × M ⊙ (and M Bh d ≈ µas ) fitted the data.But with this value of M BH , ˙ M drops by a factor of two and so P jet < ergs − . Consequently, the SANE model with a ∗ − . 94 and R high = 1 wasfinally rejected. So, eventually the conclusion was: it is unlikely that the 2017data capture an a ∗ − . 94 and R high = 1 SANE model, namely, it is unlikelythat the 2017 EHT data capture a M BH ≈ . × M ⊙ black hole.Moreover, for SANE and MAD models that produced sufficiently powerfuljets and were consistent with the 2017 EHT data, P jet was found to be driven bythe extraction of black hole spin energy through the Blandford-Znajek process. The Kerr black hole is rotating like a conductor in a magnetic field and the totaljet power is: P jet = k π Φ BH Ω , (6)where k ≈ . 045 is a numerical constant which depends on the magnetic field,Φ BH is given by equation (2), Ω is the angular velocity of the horizon:Ω = a ∗ c r + and r + is given by equation (3). P jet increases quadratically with both the black hole spin a ∗ and the mag-netic flux Φ BH , where the spin − < a ∗ < 1. Hence, GRMHD models with P jet < ergs − and zero spin a ∗ = 0 are outright rejected. For a ∗ = 0 thebright section of the ring creates a nearly symmetric ring, which is inconsistentwith what is seen in the 2017 EHT consensus image [14], pp. 9-10, p. 13-15;[5], pp. 2-3. In 1969 Roger Penrose suggested that rotational energy can be extracted from the rotatingKerr black hole [26], p. 1160. In 1977, Roger Blandford and Roman Znajek extended Penrose’s“mechanical extraction of energy” process to electromagnetic extraction of energy from a Kerrsupermassive black hole in a MHD environment [2], p. 434, p. 451. The Kerr black hole hypothesis and alterna-tive hypotheses The angular gravitational radius and ring diameter. The next stageof the experiment was obtaining the angular gravitational radius θ g by threedifferent methods – GRMHD model fitting, geometric model fitting and imagedomain feature extraction; and estimating the ring diameter θ d by the two lattermethods:1) Geometric model fitting : Two kinds of geometric crescent models (called xs-ring and xsringauss ) – collectively named, the generalized crescent model (GC) – were developed and compared directly with the 2017 EHT data. Onemodel was compared with data using the dynesty Python Bayesian dynamicNS sampling code while the other was fitted to data by THEMIS . Both THEMIS and dynesty produced the following mean value for the ring diameter of thetwo geometric crescent models: θ d ≈ µas .The GC model does not provide any scientific explanation for the 2017 EHTdata because no underlying mechanism based on physics is responsible for thestructures in it. The parameters of the GC model are therefore calibrated,i.e. fitted, to the parameters of the GRMHD models. The crescent models areassociated with the emission surrounding the shadow of a black hole. If thegeometric crescent is formed by gravitational lensing, the angular diameter ofthe photon ring obeys the equation: θ d = αθ g . (7) α represents the gravitational lensing factor and θ g is defined by equation (5). dynesty produced a ring diameter of θ d ≈ . µas for the xs-ring model and THEMIS produced θ d ≈ . µas for the xs-ringauss model. Those values werethen compared with the known value of θ g that went into the GRMHD simula-tions. The final inferred value is θ g = 3 . +045 − . µas [15], pp. 10-13.2) GRMHD model fitting : GRMHD snapshot images were fit directly todata by THEMIS and GENA (see Section 3). The combined value for the analysisperformed by both THEMIS and GENA is: θ g = 3 . +039 − . µas . NS sampling is an Approximate Bayesian Computation method. In Bayesian statistics,we start with Bayes’ theorem and update the prior probability distribution of the modelparameters upon receiving new data to obtain the posterior probability distribution of theparameters. NS is designed to evaluate the Bayesian evidence Z but as a by-product it canfurther sample the posterior probability distribution. Z is calculated by sampling nestedpoints. N live points are sampled from the prior space. At each iteration, the live point withthe lowest likelihood L i among the live points is found and a new live point is sampled. If L i +1 ≥ L i , the old live point with L i is rejected but its values are stored to calculate Z .Dynamic NS ( dynesty ) has been developed to increase the accuracy of nested sampling, tosort likelihoods more efficiently than NS and speed up the process [15], p. 4, p. 6. This led to mean values of α : α = 11 . 55 for the xs-ring model and α = 11 . 50 for the xs-ringauss model. The two θ d measurements were combined with the two α values to arriveat values of θ g using equation (7): . µas . and . µas . . Image domain feature extraction : The values of θ d obtained by imagedomain feature extraction (see end of Section 2) were converted to the θ g usingthe scaling factor α [Equation (7)], following a similar procedure to the oneused in the geometric model fitting. The following value of θ g was obtained: θ g = 3 . +042 − . µas .Fitting geometric models to data and extracting feature parameters in theimage domain both allowed quantifying the following properties of the objectat the center of M87: an angular ring diameter of θ d ≈ ± µas , an angulargravitational radius of θ g ≈ . ± . µas , a deep central brightness depression(the fractional central brightness: the ratio of the mean brightness interior tothe ring to the mean brightness around the ring), and P A . In the sixth letterit is concluded: “All of these features support the interpretation that we areseeing emission from near the event horizon that is gravitationally lensed into acrescent shape near the photon ring” [15], pp. 20-21.Prior measurements based on stellar dynamics had produced the value θ g =3 . +060 − . µas . This value is consistent with the values calculated by the EHTproject. On the other hand, gas dynamics measurements led to a lower value: θ g = 2 . +048 − . µas .It is remarked in the sixth letter that “All of the individual θ g estimates usethe GRMHD simulation library, either through directly fitting GRMHD snap-shots to the data [. . . GRMHD model fitting] or through calibration of diameters[ θ g ] resulting from geometric models or reconstructed images”, i.e. from geo-metric crescent models or image domain feature extraction. Hence “A degreeof caution is therefore warranted. The measurements rely on images generatedfrom GRMHD simulations and should be understood within that context” [13],pp. 27-30; [14], p. 2; [15], p. 1, pp. 4-21, p. 31, p. 39. The mass of the black hole. In the first letter it is noted that “A basicfeature of black holes in GR is that their size scales linearly with mass” [10],p. 9. The estimation of the angular ring diameter of θ d ≈ ± µas shouldtherefore allow for the determination of the mass M BH of the core of M87.In 1973, James Maxwell Bardeen found that the black hole casts a shadowon the hot gas that surrounds it. The diameter of the apparent shadow D sh seen by a distant observer depends on the gravitational lensing α around theblack hole. For a Schwarzschild black hole: D sh = 2 √ R g ≈ . R g where α = 2 √ 27. However, in the vicinity of a rotating Kerr black hole, “the effect ofthe frame dragging induced by the angular momentum of the Kerr black holeis quite apparent” [1], pp. 230-233. Thus, for a Kerr black hole: D sh < √ R g ≈ . R g , R sh < √ R g ≈ . R g . (8)In the GRMHD images: D sh = 9 . M BH . The Lense-Thirring effect due to the black hole rotation acts to compress the shadow withrespect to the rotation axis while the quadruple moment of the rotating black hole causes anoblate shape of the shadow. The two effects approximately cancel each other out and we areleft with a nearly circular shadow. R g is given by equation (4). Combining equation (8) with equa-tion (5) gives: θ d ≈ √ R g d ≈ . R g d ≡ . GM BH dc = αθ g . (9)Inserting θ d ≈ ± µas and d = 16 . ± . M BH .It was shown that θ d is consistent with a mass of M Bh ≈ . ± . × M ⊙ .Recall that measurements based on stellar dynamics had produced the value: M Bh ≈ . × M ⊙ [16]. This estimation is consistent with the one calculatedby the EHT project. On the other hand, gas dynamics measurements had ledto a lower value of M Bh ≈ . × M ⊙ [32], see Section 4.In the fifth letter it is stressed: “Although our working hypothesis has beenthat M87 contains a Kerr black hole, it is interesting to consider whether or notthe data is also consistent with alternative models for the central object” [14],p. 17.One such alternative model is a black hole that is spinning more rapidlythan the Kerr bound, defined as follows: a ∗ ≤ M BH or J ≤ M BH ( J ≤ GM BH c )see equations (1) and (3). Those black holes are super-spinning black holesand are called superspinars. Their horizon would disappear if J = a ∗ and thiswould imply the existence of a naked singularity and the violation of causality(spinning faster than the speed of light). Computer simulations show that theshadows of superspinars are significantly smaller compared with those of Kerrblack holes [14], p. 18.Hence, there exist solutions of the field equations of general relativity whichdescribe naked singularities not hidden by an event horizon. But the possibleexistence of these exotic solutions causes severe problems to the uniquenesstheorems. The reason is that only if all singularities are surrounded by eventhorizons, the Kerr black hole is a unique solution. So, in 1969 and 1976 RogerPenrose and Stephen Hawking phrased the censorship hypothesis, which saysthat physics censors naked singularities by always enshrouding them with ahorizon [26], p. 1160, p. 1162; [21], p. 2461.To verify the censorship hypothesis, we should demonstrate that the core ofM87 is not a naked singularity/superspinar. There also exist other horizonlesssolutions of the field equations such as rotating wormholes. According to equa-tion (8), for a Kerr black hole: R sh ≈ . R g . A 6 . × ⊙ rotating wormholehas half as big a shadow radius as a 6 . × ⊙ black hole: R sh ≈ . R g . Thisis about the same size as the shadow of the 3 . × ⊙ black hole. Hence, fora 3 . × ⊙ black hole we would get a smaller shadow than for a 6 . × ⊙ black hole. A 6 . × ⊙ naked singularity (superspinar) has an even smallershadow radius of R sh = R g .The different shadow sizes ( R sh ) were then overlaid on top of the April 112017 EHT fiducial images from each imaging pipeline (the consensus image).The exotic possibilities were ruled out and one was left with a ring that nearlyperfectly matches that of a 6 . × ⊙ black hole [10], pp. 8-9; [14], p. 18; [23].16ut there is a fly in the ointment because demonstrating that the core ofM87 has an event horizon does not conclusively disprove the existence of nakedsingularities elsewhere [28], p. 77.In the first letter it is remarked that “However, other compact-object can-didates need to be analyzed with more care”. And in the fifth letter it is againstressed: “Future observations and more detailed theoretical modeling, com-bined with multiwavelength campaigns and polarimetric measurements, willfurther constrain alternatives to Kerr black holes”. It is further noted that“the comparisons carried out here must be considered preliminary. Neverthe-less, they show that the EHT2017 observations are not consistent with severalof the alternatives to Kerr black holes” [10], pp. 8-9; [14], p. 18. A null hypothesis test, which consists of three ingredients, was subsequentlyperformed:1) The dynamical measurements provide an accurate determination of M BH .2) The shadow in the 2017 EHT image is a black hole shadow.3) The space-time of the black hole is described by the Kerr solution. Ingredient 1 : An estimation was performed of the difference between themeasurement of θ g performed by the EHT Collaboration and prior measure-ments of θ dyn : δ ≡ θ g θ dyn − θ g θ g = θ g θ dyn − . (10)For gas dynamics: δ ≈ . 78 and for stellar dynamics: δ ≈ − . 01. In the sixthletter it is written that the fact that the EHT measurement of θ g is consistentwith one of the measurements “allows us to conclude that our null hypothesishas not been violated” [15], pp. 22-23. Ingredient 2 : Are black holes described entirely by their mass M BH andspin a ∗ , or do they have hair (are they described by other parameters)? Toanswer this question, we have to know M BH because the size of the shadowis proportional to M BH . Violations of the above no-hair theorem genericallychange the shape and size of the shadow of the black hole. In other words, forKerr black holes of known M BH , the size and shape of the shadow remain nearlyunchanged and shadows always appear nearly circular. Detecting a shadow andextracting its characteristic properties offers a chance to constrain the space-time metric. For a black hole of known mass M BH and distance d from Earth,identifying the presence of the shadow and confirming that its size is in thenarrow range (4 . − . M BH constitutes a statistical null hypothesis test ofthe Kerr black hole [28], pp. 77-79; [29], p. 1; [15], p. 2; [23]. As said at theend of section 5, different R sh were overlaid on top of the consensus image. The17ing of the 2017 EHT image nearly perfectly matches that of an R sh ≈ . M BH black hole whose mass is M BH ≈ . ± . × M ⊙ . Ingredient 3 : In the fifth letter, it is explained: “we now adopt the work-ing hypothesis that M87 contains a turbulent, magnetized accretion flow sur-rounding a Kerr black hole. To test this hypothesis quantitatively against theEHT2017 data we have generated a Simulation Library of 3D time-dependentideal GRMHD models” [14], p. 3. And: “all [GRMHD] models assume a Kerrblack hole space-time, but there are alternatives” [14], p. 15. It is shown thatGRMHD models that assume a Kerr metric fit the 2017 EHT observations (seeSection 3) and it is concluded that the space-time of the black hole is describedby the Kerr metric.Finally, in the fifth letter, three images are placed one next to the other: asnapshot image based on a (spin-away) GRMHD model of a Kerr black hole,a snapshot image based on a (spin-away) GRMHD model of a Kerr black hole(restored with a FWHM Gaussian 20 µas beam), and the 2017 EHT April 6image. One can see that the two blurred images are almost the same [10], p. 6;[14], p. 2, pp. 5-6, p. 8, p. 10, p. 15. It is written in the first letter of the EHT Collaboration: ”Altogether, theresults derived here provide a new way to study compact-object spacetimesand are complementary to the detection of gravitational waves from coalescingstellar-mass black holes with LIGO/Virgo [10], p. 9. I shall now discuss thedetection of gravitational waves with Laser Interferometer Gravitational WaveObservatory (hereafter LIGO)/Virgo interferometer.A paper, “Testing the No-Hair Theorem with GW150914” [22], was pub-lished at about the same time as the six letters published in The AstrophysicalJournal Letters [10]-[15]. The paper presents an analysis of gravitational-wavedata from the first LIGO detection of the binary black-hole merger GW150914. Two stellar-mass black holes that merge, form a single distorted compactobject that gradually settles to a final stationary form. Gravitational waves areemitted throughout the entire process, at each moment carrying informationabout the evolving compact object. There are three stages in the coalescence ofthe two black holes:1) Inspiral : a long phase in which the two black holes are still quite far onefrom each other but are slowly orbiting one another in a quasi-circular orbit.Since we are dealing with weak gravitational fields, this phase allows an analytic The gravitational-waves signals are surrounded by noise. Gravitational-wave signals areextracted from the background noise using statistical significance tests and ”templete wave-forms” (model) fitting to gravitational-wave data. The gravitational waves from the mergerGW150914 were so loud that they were visible in the data even with minimal data processing. Merger : the distance between the two black holes gets smaller, the or-bit gradually shrinks and the two bodies finally merge. Numerical relativity(numerical simulations) is required. That is because the gravitational field isso strong and also time-dependent. During this phase, the amplitude of thegravitational waves gradually increases until it reaches a maximum.3) Ringdown : the newly created object releases its final gravitational wavesignals away into endless space. It wobbles and oscillates during which it ringslike a bell with characteristic frequencies and damping times determined entirelyby the mass and spin of the black hole. This stage is treated analytically usingperturbation theory. A linearly perturbed Kerr black hole emits gravitationalwaves in the form of exponential damped sine waves, with specific frequenciesand decay rates determined exclusively by the black hole’s mass and spin.The ringdown phase consists of a superposition of quasi-normal modes. Eachquasi-normal mode has a characteristic complex angular frequency: the real partis the angular frequency and the imaginary part is the inverse of the dampingtime. These modes are distinguished by their longitudinal and azimuthal in-dices, l and m respectively, as well as by their overtone number n . Ringdownovertones are the quasi-normal modes with the fastest decay rates. Each modehas a particular frequency and decay rate which are functions of the Kerr blackhole parameter spin and total mass of the black hole that is being perturbed.Numerical simulations have demonstrated that the fundamental mode l = m = 2seems to dominate the ringdown signal [3], p. 124018-18, p. 124018-21.In 2016, the LIGO Scientific and Virgo Collaborations announced the firstjoint detection of gravitational waves (GW150914) with both the LIGO andVirgo detectors. In 2018, they reported of several quantitative tests made onthe gravitational-wave data from the detection of GW150914. The purpose ofthe tests was to validate GR. The result of the tests indicates that the entireGW150914 inspiral-merger-ringdown (IMR) waveform does not deviate fromthe predictions of a binary black-hole merger in classical general relativity [25],pp.221101-3-221101-5.The detected gravitational-wave signal increases in frequency and amplitudein about eight cycles from 35 to 150 Hz, where it reaches a peak amplitude. Aftera time around 0 . s , the amplitude drops rapidly, and the frequency appearsto stabilize. After the peak gravitational wave amplitude is reached, the signalmakes one to two additional cycles, continuing to rise in frequency until reachingabout 250 Hz, while dropping sharply in amplitude.The most plausible explanation for this empirical evolution is gravitational-waves emission from two orbiting masses in the inspiral and merger phases. Thedrop in amplitude is consistent with a Kerr black hole. Recall that for a Kerrblack hole, the ringdown is expected to have a damping time roughly equal tothe period of oscillation (inversely equal to the frequency). For a black hole withspin χ = 0 . 7, a ringdown frequency of ≈ 260 Hz (cid:0) M ⊙ M (cid:1) and a damping time:4 ms (cid:16) M M ⊙ (cid:17) are calculated. The LIGO Scientific and Virgo Collaborations19onclude: ”the signal in the data is fully consistent with the final object being aKerr black hole with a dimensionless spin parameter χ = 0 . M ⊙ ”[24], pp. 2-3, pp. 12-13.The LIGO Scientific and VIRGO Collaborations explain that the initial be-havior of the gravitational-wave signal ”cannot be due to a perturbed systemreturning back to stable equilibrium, since oscillations around equilibrium aregenerically characterized by roughly constant frequencies and decaying ampli-tudes”. On the other hand, the GW150914 data ”demonstrate very differentbehavior. During the period when the gravitational wave frequency and am-plitude are increasing, orbital motion of two bodies is the only plausible ex-planation: there, the only ’damping forces’ are provided by gravitational waveemission, which brings the orbiting bodies closer (an ’inspiral’), increasing theorbital frequency and amplifying the gravitational wave energy output from thesystem” [24], p. 3.It is concluded: ”our inspiral–merger–ringdown test shows no evidence ofdiscrepancies with the predictions of GR” [25], p.221101-5.The LIGO Scientific and Virgo Collaborations performed a test that allowed”for possible violations of GR” and concluded that the value of parameters wasusually found to represent GR. An additional test was performed. They asked:Does GR fit the data better than alternative competing models? The followingmodel was compared with GR: a model based on theories of gravity mediated bya graviton with a nonzero mass in which the gravitational waves travel at a speeddifferent than the speed of light. In GR, gravitons are massless and travel at thespeed of light. The presence of non-GR polarization states were searched for.But it was difficult to distinguish between GR and non-GR models on the basisof GW150914 data alone. Since the Hanford and Livingston LIGO instrumentshave similar orientations, they are sensitive to a very similar linear combinationof the gravitational-wave polarizations, so it is difficult to distinguish betweenthe GR and non-GR states [25], p.221101-10.It is concluded: ”With the exception of the graviton Compton wavelengthand the test for the presence of a non-GR polarization, we did not performany studies aimed at constraining parameters that might arise from specificalternative theories” [25], p. 221101-8, pp. 221101-10-11.Testing the black hole ring at the correct frequencies and damping times, itought to be possible to test the validity of the no-hair theorem, which statesthat the remnant must be a Kerr black hole.Already in 2004, a team of astrophysicists had asked: “can gravitationalwave observations provide a test of one of the fundamental predictions of gen-eral relativity: the no-hair theorem?” They suggested “a definitive test of thehypothesis that observations of damped, sinusoidal gravitational waves originatefrom a black hole or, alternatively, that nature respects the general relativisticno-hair theorem” [7], p. 787.In 2017, three astrophysicists belonging to the LIGO Scientific and VirgoCollaborations, Eric Thrane, Paul Lasky and Yuri Levin, wrote that “The recentdetections of gravitational waves from stellar-mass black hole mergers would20eem to suggest that a test of the no-hair theorem might be around the corner”.A method was provided ”for testing the no-hair theorem using only data fromafter the remnant black hole has settled into a perturbative state”.The post-merger remnant must be allowed to settle into a perturbative,Kerr-like state and this means that the ringdown frequencies and damping timesdepend only on the mass and spin of the newly created black hole. In this way,the no-hair theorem places stringent requirements on the asymptotic behavior ofperturbed black holes. The no-hair theorem concerns itself with linear pertur-bations. But it was found that at no point in time is the post-merger waveformprecisely described by black hole perturbation theory. That is because, there isalways a contribution, however small, left over from the merger. Furthermore,the ringdown signal becomes weaker as it settles into a Kerr black hole.The authors were confronted with the following problem: they could eitherobtain higher signal-to-noise (SNR) ratio by adding louder signals from themerger phase (the main gravitational wave signal) or, wait for the remnantblack hole to settle to the perturbative state where the no-hair theorem applies.They chose the latter option because as louder signals were added, it was nolonger clear whether this improved the knowledge of the ringdown frequencyand damping times. So, they arrived at the conclusion that it may be possibleto test the no-hair theorem but the observed behavior could either be attributedto a numerical relativity artifact, or to a residual non-linearity of the signal fromthe merger decaying on a timescale comparable to the linear ringdown signal[31], pp. 102004-1-2, p. 102004-5.Matthew Giesler, Mark Scheel and Saul Teukolky have been working onthe LIGO data and gravitational waves. In May 2019, they submitted a paperwith Maximiliano Isi and Will Farr from the LIGO Scientific and Virgo Collab-orations in which they analyzed the ringdown gravitational-wave data. Theythought that a gestalt shift was needed. It does not mean that Thrane, Laskyand Levin’s reservations are not sound. It only means that one team thinksthey have solved the problem whilst the other probably holds an opposite view.So, Geisler and his team have shown that including enough overtones of themode l = 2 allows obtaining higher SNR. A GW150914-like signal was firststudied. It was found that the inclusion of enough overtones associated withthe l = m = 2 mode “provides a high-accuracy description of the ringdown”,where the high SNR “can be exploited to significantly reduce the uncertainty inthe extracted remnant properties” [17], p. 041060-2, p. 041060-8, p. 041060-10.Previously, overtones had been believed to be too faint to be detected and itwas believed that one had to wait at least ten years to test the no-hair theorem.But as shown above, studies done by the team have shown that although theovertones decay very quickly, the first overtones of GW150914 should be loudenough to be detected.Measuring the quasi-normal modes from gravitational-wave observations is A simulated output of a LIGO-like detector was studied in response to the same gravita-tional waves as the ones from the asymptotic remnant. That is, the l = m = 2 mode of thesignal was injected into simulated Gaussian noise corresponding to the sensitivity of AdvancedLIGO in its design configuration. l = m = 2. The GW150914 ringdown using this mode and its first overtone wereanalyzed. These are ringdown-only measurements. The ringdown-only measure-ments of the remnant mass and spin magnitude were then compared to thoseobtained from the analysis of the entire GW150914 inspiral-merger-ringdown(IMR) waveform. It was concluded that evidence of the mode l = m = 2 andat least one overtone was found and, a 90%-credible measurement of the rem-nant mass and spin was obtained in agreement with that inferred from the fullwaveform.Measuring the frequencies of the fundamental and first overtone, informationwas extracted about the GW150914 remnant and ”their consistency with theKerr hypothesis” was established. It was concluded that the GW150914 merger”produced a Kerr black hole as described by general relativity” [22], p. 111102-5.It is stressed at the end of Isi et al.’s paper that, as the precision of thedetectors improves, it can be expected that using overtones will provide bettertests of the no-hair theorem [22], p. 111102-1, p. 111102-3, p. 111102-5. The first question asked by the EHT Collaboration is: Does M87’s core have ahorizon? Is the object at the center of the galaxy M87 a spinning Kerr blackhole as predicted by general relativity?In order to answer this question, the EHT Collaboration first endorsed theworking hypothesis that the central object is indeed a black hole described bythe Kerr metric. They chose this hypothesis based on previous research andobservations of the galaxy M87. In 2015 a team of scientists belonging to theEHT Collaboration made an experiment the goal of which was to compare themerits of two rival hypotheses: a compact object with a surface and a black holewith a horizon. The black hole hypothesis was selected as the best explanationof the evidence.The EHT Collaboration tested the Kerr black hole hypothesis and foundthat it was consistent with the evidence. How did they test the Kerr black holehypothesis? GRMHD models based on the Kerr metric were used to extractparameters from the 2017 EHT data (see Sections 3, 4 and 5) and then it wasshown that the data confirm the hypothesis that the compact object at thecenter of M87 is a supermassive Kerr rotating black hole (see Section 6). Thesixth letter ends with the following statement: “Together, our results strongly22upport the hypothesis that the central object in M87 is indeed a Kerr blackhole” [15], p. 23.Ian Hacking once said: “This looks like a classic example of what philoso-phers, following Gilbert Harman ([20]) have come to call inference to the bestexplanation (IBE)”. He added: “there is an overall conjecture of the sort thatPopper would have called metaphysical” ([19], pp. 568-569). In our case study,in the fifth letter it is written: “the results provided here are consistent with theexistence of astrophysical black holes” ([14], p. 19). Hacking and Wesley Salmonare on the same page when it comes to supermassive black holes. They haveargued that scientific existence claims are always open to question. When onesays that astrophysical black holes exist, it adds nothing to our understandingand to the explanation. The fact that the black hole hypothesis explains theobservations does not provide evidence that black holes exist. Existence claimswith respect to black holes are not part of the explanation [18], pp. 52-54; [30],p. 56, p. 58.The Kerr black hole hypothesis has explanatory power in accounting for: in-gredient 2 , ingredient 3 (see Sections 6 and 3) and the GW150914 Ringdown. Itis also the best explanation of the evidence for M87’s core and for the GW150914gravitational wave event. Does it mean that it is also true? If truth means thatno other hypothesis will explain the evidence as well as the Kerr black hole hy-pothesis, then the answer is: we cannot say that it is true. The reason is that theEHT Collaboration has written: “Future observations and more detailed theo-retical modeling, combined with multiwavelength campaigns and polarimetricmeasurements, will further constrain alternatives to Kerr black holes” [14], p.18; see the end of Section 5. And Isi et al. write: ”Future studies of black-holeringdowns relying on overtones could potentially allow us to identify black-holemimickers”, that is, exotic alternatives to the Kerr black hole hypothesis, ”andprobe the applicability of the no-hair theorem with high precision, even withexisting detectors”. This would ”lead to more specific predictions from generalrelativity” [22], p. 111102-5. Doeleman has said: ”Now if we could make an image of this object, then wecould test Einstein’s theories of gravity in the one place where they might breakdown in the universe” [6]. Can we also test Hawking radiation in the one placewhere Einstein’s theory of gravity breaks down?Hawking pointed out that evaporation violates the classical censorship hy-pothesis. Hawking explained that if one tries to describe the process of a blackhole losing mass and eventually disappearing and evaporating by a classicalspace-time metric, then “there is inevitably a naked singularity when the black Salmon wrote: astrophysicists believe that there is a black hole at the center of our galaxy.But he was not convinced of this particular existence claim and he added that Hacking was“skeptical far more generally about black holes”. From what emerges from Hacking’s papers,he is indeed skeptical about black holes. years, then according toHawking’s hypothesis at the time at which the EHT experiment was performedin 2017, the compact object at the center of M87 could not be a naked singu-larity. And according to Hawking’s theory, it will have a horizon for manyyears to come. Paradoxically, Hawking’s above hypothesis can explain at leastas well the evidence as the no-hair theorem. Although according to Hawking,a supermassive black hole will gradually evaporate through Hawking radiation,the rate of this evaporation is so slow that we cannot detect it. Collecting ad-ditional and more accurate data from the object at the center of M87 will notbe enough to detect Hawking radiation.That is exactly the point raised by Bas van Fraassen: “Is the best explanationwe have, likely to be true?” He answers this question in the negative saying thatthere are many possible theories, perhaps never yet formulated, but that can fitall the evidence so far. These theories can explain at least as well the evidenceas the best theory we have now. But with respect to statements that go beyondthe evidence we possess today these theories disagree with one another. Weconsider them to be false because of underdetermination of theory by evidence.Classical general relativity and the no-hair theorem are our best explanation andthey belong to the class of explanations that can fit all the evidence to date, butthey also disagree with certain quantum gravity theories, theories with quantumcorrections to classical general relativity [9], pp. 160-161. References [1] Bardeen, J. M. (1973). ”Timelike and Null Geodesics in the Kerr Metric.”In DeWitt C. and DeWitt B. S. (eds.). Black Holes Les Astres Occlus. NewYork: Gordon and Breach Science Publishers, pp. 216-239.[2] Blandford, R. D. and Znajek, R. L. (1977). “Electromagnetic extraction ofenergy from Kerr black holes.” Monthly Notices of the Royal AstronomicalSociety Physical Review D The evaporation time t for the black hole, from the point of view of an outside observer,is proportional to the cube of the mass of the black hole: t = πG M BH ¯ hc [34], p. 18. 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