Emanuele Berti

Quasinormal modes of black holes and black branes

Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra require solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field.

Testing general relativity with present and future astrophysical observations

One century after its formulation, Einsteins general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteins theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

Low-frequency gravitational-wave science with eLISA/NGO

We review the expected science performance of the New Gravitational-Wave Observatory (NGO, a.k.a. eLISA), a mission under study by the European Space Agency for launch in the early 2020s. eLISA will survey the low-frequency gravitational-wave sky (from 0.1 mHz to 1 Hz), detecting and characterizing a broad variety of systems and events throughout the Universe, including the coalescences of massive black holes brought together by galaxy mergers; the inspirals of stellar-mass black holes and compact stars into central galactic black holes; several millions of ultra-compact binaries, both detached and mass transferring, in the Galaxy; and possibly unforeseen sources such as the relic gravitational-wave radiation from the early Universe. eLISAs high signal-to-noise measurements will provide new insight into the structure and history of the Universe, and they will test general relativity in its strong-field dynamical regime.

COSMOLOGICAL BLACK HOLE SPIN EVOLUTION BY MERGERS AND ACCRETION

Using recent results from numerical relativity simulations of black hole mergers, we revisit previous studies of cosmologicalblackholespinevolution.Weshowthatmergersareveryunlikelytoyieldlargespins,unlessalignment of the spins of the merging holes with the orbital angular momentum is very efficient. We analyze the spin evolution in three specific scenarios: (1) spin evolves only through mergers, (2) spin evolves through mergers and prolonged accretion episodes, and (3) spin evolves through mergers and short-lived (chaotic) accretion episodes. We study how different diagnostics can distinguish between these evolutionary scenarios, assessing the discriminating power of gravitational-wave measurements and X-ray spectroscopy. Gravitational radiation can produce three different types of spin measurements, yielding, respectively, the spins of the two black holes in a binary inspiral prior to merger, the spin of the merger remnant (as encoded in the ring-down waves), and the spin of ‘‘single’’ black holes during the extrememass-ratioinspiral(EMRI)of compactobjects.Thelatterspinpopulationisalsoaccessibletoiron-linemeasurements. We compute and compare the spin distributions relevant for these different observations. If iron-line measurements and gravitational-wave observations of EMRIs only yield dimensionless spins j ¼ J/M 2 > 0:9, then prolonged accretion should be responsible for spin-up, and chaotic accretion scenarios would be very unlikely. If only a fraction of the whole population of low-redshift black holes spins rapidly, spin-alignment during binary mergers (rather than prolonged accretion) could be responsible for spin-ups. Subject headingg black hole physics — cosmology: theory — galaxies: evolution — gravitational waves Online material: color figures

Gravitational-wave spectroscopy of massive black holes with the space interferometer LISA

Newly formed black holes are expected to emit characteristic radiation in the form of quasinormal modes, called ringdown waves, with discrete frequencies. LISA should be able to detect the ringdown waves emitted by oscillating supermassive black holes throughout the observable Universe. We develop a multimode formalism, applicable to any interferometric detectors, for detecting ringdown signals, for estimating black-hole parameters from those signals, and for testing the no-hair theorem of general relativity. Focusing on LISA, we use current models of its sensitivity to compute the expected signal-to-noise ratio for ringdown events, the relative parameter estimation accuracy, and the resolvability of different modes. We also discuss the extent to which uncertainties on physical parameters, such as the black-hole spin and the energy emitted in each mode, will affect our ability to do black-hole spectroscopy.

Geodesic stability, Lyapunov exponents, and quasinormal modes

Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability time scale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black-hole background are unstable, and (ii) the instability time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d ≥ 6.

Double Compact Objects III: Gravitational Wave Detection Rates

The unprecedented range of second-generation gravitational-wave (GW) observatories calls for refining the predictions of potential sources and detection rates. The coalescence of double compact objects (DCOs)?i.e., neutron star?neutron star (NS?NS), black hole?neutron star (BH?NS), and black hole?black hole (BH?BH) binary systems?is the most promising source of GWs for these detectors. We compute detection rates of coalescing DCOs in second-generation GW detectors using the latest models for their cosmological evolution, and implementing inspiral-merger-ringdown gravitational waveform models in our signal-to-noise ratio calculations. We find that (1) the inclusion of the merger/ringdown portion of the signal does not significantly affect rates for NS?NS and BH?NS systems, but it boosts rates by a factor of ?1.5 for BH?BH systems; (2) in almost all of our models BH?BH systems yield by far the largest rates, followed by NS?NS and BH?NS systems, respectively; and (3) a majority of the detectable BH?BH systems were formed in the early universe in low-metallicity environments. We make predictions for the distributions of detected binaries and discuss what the first GW detections will teach us about the astrophysics underlying binary formation and evolution.

Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis

We study the inspiral, merger, and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M2/M1=1 to q=4). We compare numerical and post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the post-Newtonian series to the numerical results is nonmonotonic. To leading order, the total energy emitted in the merger phase scales like η2 and the spin of the final black hole scales like η, where η=q/(1+q)2 is the symmetric mass ratio. We study the multipolar distribution of the radiation, finding that odd-l multipoles are suppressed in the equal mass limit. Higher multipoles carry a larger fraction of the total energy as q increases. We introduce and compare three different definitions for the ringdown starting time. Applying linear-estimation methods (the so-called Prony methods) to the ringdown phase, we find resolution-dependent time variations in the fitted parameters of the final black hole. By cross correlating information from different multipoles, we show that ringdown fits can be used to obtain precise estimates of the mass and spin of the final black hole, which are in remarkable agreement with energy and angular momentum balance calculations.

Double Compact Objects II: Cosmological Merger Rates

The development of advanced gravitational wave (GW) observatories, such as Advanced LIGO and Advanced Virgo, provides impetus to refine theoretical predictions for what these instruments might detect. In particular, with the range increasing by an order of magnitude, the search for GW sources is extending beyond the local universe and out to cosmological distances. Double compact objects (neutron star-neutron star (NS-NS), black hole-neutron star (BH-NS), and black hole-black hole (BH-BH) systems) are considered to be the most promising GW sources. In addition, NS-NS and/or BH-NS systems are thought to be the progenitors of gamma-ray bursts and may also be associated with kilonovae. In this paper, we present the merger event rates of these objects as a function of cosmological redshift. We provide the results for four cases, each one investigating a different important evolution parameter of binary stars. Each case is also presented for two metallicity evolution scenarios. We find that (1) in most cases NS-NS systems dominate the merger rates in the local universe, while BH-BH mergers dominate at high redshift, (2) BH-NS mergers are less frequent than other sources per unit volume, for all time, and (3) natal kicks may alter the observable properties of populations in a significant way, allowing the underlying models of binary evolution and compact object formation to be easily distinguished. This is the second paper in a series of three. The third paper will focus on calculating the detection rates of mergers by GW telescopes.

Estimating spinning binary parameters and testing alternative theories of gravity with LISA

We investigate the effect of spin-orbit and spin-spin couplings on the estimation of parameters for inspiralling compact binaries of massive black holes, and for neutron stars inspiralling into intermediate-mass black holes, using hypothetical data from the proposed Laser Interferometer Space Antenna (LISA). We work both in Einstein’s theory and in alternative theories of gravity of the scalar-tensor and massive-graviton types. We restrict the analysis to non-precessing spinning binaries, i.e. to cases where the spins are aligned normal to the orbital plane. We find that the accuracy with which intrinsic binary parameters such as chirp mass and reduced mass can be estimated within general relativity is degraded by between one and two orders of magnitude. We find that the bound on the coupling parameter ωBD of scalar-tensor gravity is significantly reduced by the presence of spin couplings, while the reduction in the graviton-mass bound is milder. Using fast Monte-Carlo simulations of 10 4 binaries, we show that inclusion of spin terms in massive blackhole binaries has little effect on the angular resolution or on distance determination accuracy. For stellar mass inspirals into intermediate-mass black holes, the angular resolution and the distance are determined only poorly, in all cases considered. We also show that, if LISA’s low-frequency noise sensitivity can be extrapolated from 10 −4 Hz to as low as 10 −5 Hz, the accuracy of determining both extrinsic parameters (distance, sky location) and intrinsic parameters (chirp mass, reduced mass) of massive binaries may be greatly improved.