Fast Radio Bursts and White Hole Signals
FFast Radio Bursts and White Hole Signals
Aur´elien Barrau a , Carlo Rovelli b and Francesca Vidotto b,c a Laboratoire de Physique Subatomique et de Cosmologie, Universit´e Grenoble-Alpes,CNRS-IN2P3 53, avenue des Martyrs, F-38026 Grenoble, France b CPT, Aix-Marseille Universit´e, Universit´e de Toulon,CNRS, and the Samy Maroun Research Center for Time,Space and the Quantum, Case 907, F-13288 Marseille, France. c Radboud University, Institute for Mathematics, Astrophysics and Particle Physics,Mailbox 79, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands. (Dated: September 25, 2014)We estimate the size of a primordial black hole exploding today via a white hole transition, andthe power in the resulting explosion, using a simple model. We point out that Fast Radio Bursts,strong signals with millisecond duration, probably extragalactic and having unknown source, havewavelength not far from the expected size of the exploding hole. We also discuss the possible higherenergy components of the signal.
I. THE MODEL
The fate of the vast amount of matter fallen into blackholes is unknown. A possibility investigated by numer-ous authors is that quantum gravity generates pressure(or weakens gravity) halting the collapse and triggering abounce causing the black hole to explode [1–19] possiblyat a size much larger than Planckian [20–22]. Lifetimesof stellar or galactic holes are far too long for us to have achance to detect the resulting explosion. But primordialblack holes formed in the very early universe, if they ex-ist [23–26], could be exploding today. For a black hole ofinitial mass m , the hypothesis that the phenomenon pre-vents the firewall problem [27] implies a maximal lifetimeshorter than the Hawking evaporation time [28], but stillof order m in Planck units ( c = (cid:126) = G = 1). In [22], thesignal emitted by a primordial black hole exploding todaywas estimated, under this maximal lifetime hypothesis,to be in the Gev range. The phenomenology of such anevent has been studied in [29]. For related suggestionssee [30–36].Later theoretical work on the gravitational field of suchbouncing “Planck star” has pointed out that quantumgravity effects might become relevant earlier, allowingfor shorter blackhole lifetime [37]. Classical general rela-tivity outside the region of the hole is compatible with ablack-to-white quantum transition. The black and whitehole solutions of the Einstein equations can be glued andtheir singularities replaced by a finite (in space and intime) non-classical tunnelling region. An estimate of thetime needed to exit the semiclassical regime yields a blackhole lifetime of the order τ = 4 k m (1)in Planck units, where k is estimated to k = .
05 in [37].Primordial black holes of initial mass around m = (cid:114) t H k ∼ . × kg (2) where t H is the Hubble time, can therefore be expected toexplode today. The possibility of observing signals fromwhite holes was first pointed out long ago by Narlikar,Appa Rao and Dadhich in [38].A “bounce” can take a cosmological time because ofthe general-relativistic time dilation: the proper timeof an observer outside the hole is cosmological, but theproper time of an observer bouncing with the star inside the hole is very small (order m , namely the time lighttakes to cross the collapsing object).If this happens, most of the energy of the black holeis still present at explosion time, because Hawking radia-tion does not have the time to consume it. The explodingobject should have a total energy of the order E = mc ∼ . × erg (3)concentrated in a size given by the correspondingSchwarzschild radius R = 2 Gmc ∼ .
02 cm (4)We may expect two main component of the signal fromsuch an explosion: (i) a lower energy signal at a wave-length of the order of the size of the exploding object.(ii) a higher energy signal which depend on the details ofthe liberated hole content. We discuss the first signal inSection II, the possibility of identifying it with observedsignals in Section III, and the second in Section IV.
II. LOW ENERGY SIGNAL
A strong explosion in a small region should emit a sig-nal with a wavelength of the order of the size of the re-gion or somehow larger, and convert some fraction of itsenergy in photons. Therefore it is reasonable to expectfrom this scenario an electromagnetic signal emitted inthe infrared λ predicted (cid:38) .
02 cm . (5) a r X i v : . [ g r- q c ] S e p z Λ FIG. 1: White hole signal wavelength (unspecified units) asa function of z . Notice the characteristic flattening at largedistance: the youth of the hole compensate for the redshift. The received signal is going to be corrected by standardcosmological redshift. However, signals coming form far-ther away were originated earlier, namely younger, andtherefore less massive, holes, giving a peculiar decreaseof the emitted wavelength with distance. The receivedwavelength, taking into account both the expansion ofthe universe and the change of time available for theblack hole to bounce, can be obtained folding (1) into therelation between redshift and proper time. This gives λ obs ∼ Gmc (1 + z ) × (6) (cid:118)(cid:117)(cid:117)(cid:116) H − k Ω / sinh − (cid:34)(cid:18) Ω Λ Ω M (cid:19) / ( z + 1) − / (cid:35) . where we have reinserted the Newton constant G andthe speed of light c while H , Ω Λ and Ω M are the Hubbleconstant, and the cosmological-constant and matter den-sities. Interestingly this is a very slowly varying functionof the redshift. The redshift slightly over-compesates forthe effect of the hole’s age. The signal varies by lessthan an order of magnitude for redshifts up to the de-coupling time (z=1100). See Figure 1. If the redshift ofthe source can be estimated by using dispersion measures(or by identifying a host galaxy) this would be a smokinggun evidence for the phenomenon.Do we have detectors for these signals? There are de-tectors operating at such wavelengths, beginning by therecently launched Herschel instrument. The 200 micronrange can be observed both by PACS and SPIRE. Theformer employs four detector arrays, two bolometer ar-rays and two Ge:Ga photoconductor arrays. The lat-ter is a camera associated with a low to medium resolu-tion spectrometer complementing PACS. It comprises animaging photometer and a Fourier Transform Spectrom-eter (FTS), both of which use bolometer detector arrays.The predicted signal falls in between PACS and SPIREsensitivity zones. There is also a very high resolution het-erodyne spectrometer, HIFI, onboard Herschel, but thisis not an imaging instrument, it observes a single pixelon the sky at a time.However, the bolometer technology makes detecting short white-hole bursts difficult. Cosmic rays cross thedetectors very often and induce glitches that are removedfrom the data. Were physical IR bursts due to bounc-ing black hole registered by the instrument, they wouldmost probably have been flagged and deleted, mimickinga mere cosmic ray noise.There might be room for improvement. It is not im-possible that the time structure of the bounce could leadto a characteristic time-scale of the event larger thanthe response time of the bolometer. In that case, aspecific analysis should allow for a dedicated search ofsuch events. We leave this study for a future work asit requires astrophysical considerations beyond this firstinvestigation. An isotropic angular distribution of thebursts, signifying their cosmological origin, could alsobe considered as evidence for the model. In case manyevents were measured, it would be important to ensurethat there is no correlation with the mean cosmic-ray flux(varying with the solar activity) at the satellite location.Let us turn to something that has been observed. III. FAST RADIO BURSTS
Fast Radio Bursts are intense isolated astrophysicalradio signals with a duration of milliseconds. A smallnumber of these were initially detected only at the Parkesradio telescope [39–41]. Observations from the AreciboObservatory have confirmed the detection [42]. The fre-quency of these signals is in the order of 1 . λ observed ∼
20 cm . (7)These signals are believed to be of extragalactic origin,mostly because the observed delay of the signal arrivaltime with frequency agrees quite well with the dispersiondue to a ionized medium, expected from a distant source.The total energy emitted in the radio by a source is esti-mated to be of the order 10 erg. The progenitors andphysical nature of the Fast Radio Bursts are currentlyunknown [42].There are three orders of magnitude between the pre-dicted signal (5) and the observed signal (7). But theblack-to-white hole transition model is still very rough. Itdisregards rotation, dissipative phenomena, anisotropies,and other phenomena, and these could account for thediscrepancy.In particular, astrophysical black holes rotate: one mayexpect the centrifugal force to lower the attraction andbring the lifetime of the hole down. In turn, this shouldallow larger black holes to be exploding today, and signalsof larger wavelength. Furthermore, we have not taken theastrophysics of the explosion into account. (The totalenergy (3) available in the black hole according to thetheory is largely sufficient –9 orders of magnitude larger–than the total energy emitted in the radio estimated bythe astronomers.)Given these uncertainties, the hypothesis that Fast Ra-dio Burst could originate from exploding white holes istempting, and we think deserves to be explored. IV. HIGH ENERGY SIGNAL
When a black hole radiates by the Hawking mecha-nism, its Schwarzschild radius is the only scale in theproblem and the emitted radiation has a typical wave-length of this size. In the model considered here, onthe other hand, the emitted energy does not come fromthe coupling of the event horizon with the vacuum quan-tum fluctuations, but rather from the time-reversal of thephenomenon that formed (and possibly, filled) the blackhole. Therefore the emitted signal can be characterisedby another scale: that characteristic of the matter thatentered in the hole. Since the proper time of the bounce inside the black hole is very short, there is no reason toexpect this to vary much during the cosmological time.In most simple models, primordial black holes formwith a mass of the order of the Hubble Mass, M H ≈ t in Planck units, at formation time. For black holes withmasses as considered in this work, that is around 10 kg,this corresponds to a temperature of the Universe of theorder of a TeV. It is natural to assume that a fractionof the energy of the photons emitted from the bouncinghole be of this order of magnitude.The bouncing hole acts as “redshift freezing machine”for fields inside: they are emitted back at the energy theyhad when absorbed. In the meanwhile, the redshift of thesurrounding universe has grown tremendously.Gamma-ray bursts are known at much lower energiesthan a TeV. Although some analysis were already carriedout, no burst in the TeV range has been observed to date.Even if the rather small astrophysical background in thishigh-energy range is excellent from the viewpoint of de-tection, there is, however, a major instrumental issue:TeV detectors are ground based Cherenkov telescopesand have a very narrow field of view. The probabilityfor a burst to occur in the appropriate direction mightbe small. In addition, due to the absorption by the cos-mic infrared background, TeV photons cannot come fromfar away and the horizon is quite limited. A new genera-tion of instruments, namely the CTA experiment, is nowbeing designed with a huge array of telescopes that couldallow to monitor many portions of the sky at the sametime, opening new possibilities for this search.The redshift dependance of this signal is different fromthe IR/radio one. For a hole exploding at redshift z , cor-responding to cosmic time t , the signal energy is givenby the temperature of the universe at formation time,which is proportional to the inverse square root of theformation time. This time is in turn proportional to thehorizon mass which is (roughly) equal to the formationmass of the black hole. The emission wavelength is there-fore proportional to the square root of the mass of the black hole. This gives an observed wavelength λ obs ∝ (1 + z ) (cid:32) sinh − (cid:34)(cid:18) Ω Λ Ω M (cid:19) ( z + 1) − (cid:35)(cid:33) . (8)Measuring the redshift would require to associate the ob-served event with a host structure, which is far from beingobvious, but, in principle, this dependence on z providesa specific signature.If the fraction of the total energy as gamma-rays isdenoted x , the number of photons radiated during thebounce will be N γ ∼ xm/E γ . For x = 0 .
2, as a rea-sonable example, this leads to 10 γ -rays in the TeVrange. If one considers an effective telescope area givenby a disc of radius 100 meters (the approximate size ofthe Cherenkov shower) and requires 10 measured pho-tons for each burst, the bouncing object can be detectedup to a distance of D ≈ m, which is around 100million light-years or a redshift of z=0.01. This is withinthe γ -ray horizon and the latter is therefore not the lim-iting factor. A promising strategy could be to point thetelescope toward a galaxy with z < .
01. If it is nota blazar, the TeV background is expected to be smallor vanishing. If bouncing primordial black holes around10 kg are to represent a large fraction of the dark mat-ter, there could be as much as 10 objects of this typewithin the galaxy. Each exploding (bouncing) one wouldbe detected. Of course, the actual number of events perunit of time depends of the width of the primordial massspectrum (if any), which is not known. But orders ofmagnitude show that detection is not hopeless. V. CONCLUSION
We have discussed the signal of a primordial black holeexploding today via a black-to-white quantum transition[37] and the possibility of observing the lower as wellas the higher energies components of the signal. Wehave observed that the first would have a characteristicdistance-frequency relation flattening at large redshift.We have pointed out the possibility of identifyingthis signal with the Fast Radio Bursts observed by theArecibo and Parkes observatories.A connection between black hole explosions and shortradio signals was suggested time ago by M. Rees [43]. Thephysics considered by Rees is different from that consid-ered here: radio or optical emission from the relativisticshock wave generated from the explosion of small blackholes, interacting with an ambient magnetic field.In the scenario we have considered here, on the con-trary, the phenomenon is of direct quantum gravitationalnature. A quantum gravitational phenomenon can haveeffects at observable scales because the presence of thelarge multiplicative factor [44] t H t P ∼ × . (9)in the physics of the phenomenon.If the observed Fast Radio Bursts are connected tothis phenomenon, they represent the first known directobservation of a quantum gravitaty effect.We thank Massimo Cerdonio for suggestions and ad- vices. FV acknowledges support from the NetherlandsOrganisation for Scientific Research (NWO) Veni Fel-lowship Program, and from the Centre National de laRecherche Scientifique (CNRS) visiting program for sup-porting her visit at the CPT in Marseille. [1] V. P. Frolov and G. Vilkovisky, “Quantum Gravity re-moves Classical Singularities and Shortens the Life ofBlack Holes,” ICTP preprint IC/79/69, Trieste. (1979) .[2] C. R. Stephens, G. t. Hooft, and B. F. Whiting, “Blackhole evaporation without information loss,”
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