arXiv subjects

Emanuele Berti

Publications and source records attributed to Emanuele Berti.

At least 289 records · Page 16Linked to original sources

arXiv2007

A post-Newtonian diagnosis of quasiequilibrium configurations of neutron star-neutron star and neutron star-black hole binaries

We use a post-Newtonian diagnostic tool to examine numerically generated quasiequilibrium initial data sets for non-spinning double neutron star and neutron star-black hole binary systems. The PN equations include the effects of tidal interactions, parametrized by the compactness of the neutron stars and by suitable values of ``apsidal'' constants, which measure the degree of distortion of stars subjected to tidal forces. We find that the post-Newtonian diagnostic agrees well with the double neutron star initial data, typically to better than half a percent except where tidal distortions are becoming extreme. We show that the differences could be interpreted as representing small residual eccentricity in the initial orbits. In comparing the diagnostic with preliminary numerical data on neutron star-black hole binaries, we find less agreement.

gr-qc↗

arXiv2007

Mining information from binary black hole mergers: a comparison of estimation methods for complex exponentials in noise

The ringdown phase following a binary black hole merger is usually assumed to be well described by a linear superposition of complex exponentials (quasinormal modes). In the strong-field conditions typical of a binary black hole merger, non-linear effects may produce mode coupling. Artificial mode coupling can also be induced by the black hole's rotation, if the radiation field is expanded in terms of spin-weighted spherical (rather than spheroidal) harmonics. Observing deviations from linear black hole perturbation theory requires optimal fitting techniques to extract ringdown parameters from numerical waveforms, which are inevitably affected by errors. So far, non-linear least-squares fitting methods have been used as the standard workhorse to extract frequencies from ringdown waveforms. These methods are known not to be optimal for estimating parameters of complex exponentials. Furthermore, different fitting methods have different performance in the presence of noise. The main purpose of this paper is to introduce the gravitational wave community to modern variations of a linear parameter estimation technique first devised in 1795 by Prony: the Kumaresan-Tufts and matrix pencil methods. Using "test" damped sinusoidal signals in Gaussian white noise we illustrate the advantages of these methods, showing that they have variance and bias at least comparable to standard non-linear least-squares techniques. Then we compare the performance of different methods on unequal-mass binary black hole merger waveforms. The methods we discuss should be useful both theoretically (to monitor errors and search for non-linearities in numerical relativity simulations) and experimentally (for parameter estimation from ringdown signals after a gravitational wave detection).

gr-qc↗

arXiv2006

Quasinormal ringing of Kerr black holes: The excitation factors

Distorted black holes radiate gravitational waves. In the so-called ringdown phase radiation is emitted in a discrete set of complex quasinormal frequencies, whose values depend only on the black hole's mass and angular momentum. Ringdown radiation could be detectable with large signal-to-noise ratio by the Laser Interferometer Space Antenna LISA. If more than one mode is detected, tests of the black hole nature of the source become possible. The detectability of different modes depends on their relative excitation, which in turn depends on the cause of the perturbation (i.e. on the initial data). A ``universal'', initial data-independent measure of the relative mode excitation is encoded in the poles of the Green's function that propagates small perturbations of the geometry (``excitation factors''). We compute for the first time the excitation factors for general-spin perturbations of Kerr black holes. We find that for corotating modes with $l=m$ the excitation factors tend to zero in the extremal limit, and that the contribution of the overtones should be more significant when the black hole is fast rotating. We also present the first analytical calculation of the large-damping asymptotics of the excitation factors for static black holes, including the Schwarzschild and Reissner-Nordstrom metrics. This is an important step to determine the convergence properties of the quasinormal mode expansion.

gr-qc↗

arXiv2006

A numerical study of the quasinormal mode excitation of Kerr black holes

We present numerical results from three-dimensional evolutions of scalar perturbations of Kerr black holes. Our simulations make use of a high-order accurate multi-block code which naturally allows for fixed adaptivity and smooth inner (excision) and outer boundaries. We focus on the quasinormal ringing phase, presenting a systematic method for extraction of the quasinormal mode frequencies and amplitudes and comparing our results against perturbation theory. The amplitude of each mode depends exponentially on the starting time of the quasinormal regime, which is not defined unambiguously. We show that this time-shift problem can be circumvented by looking at appropriately chosen relative mode amplitudes. From our simulations we extract the quasinormal frequencies and the relative and absolute amplitudes of corotating and counterrotating modes (including overtones in the corotating case). We study the dependence of these amplitudes on the shape of the initial perturbation, the angular dependence of the mode and the black hole spin, comparing against results from perturbation theory in the so-called asymptotic approximation. We also compare the quasinormal frequencies from our numerical simulations with predictions from perturbation theory, finding excellent agreement. Finally we study under what conditions the relative amplitude between given pairs of modes gets maximally excited and present a quantitative analysis of rotational mode-mode coupling. The main conclusions and techniques of our analysis are quite general and, as such, should be of interest in the study of ringdown gravitational waves produced by astrophysical gravitational wave sources.

gr-qc↗

arXiv2006

Eccentricity content of binary black hole initial data

Using a post-Newtonian diagnostic tool developed by Mora and Will, we examine numerically generated quasiequilibrium initial data sets that have been used in recently successful numerical evolutions of binary black holes through plunge, merger and ringdown. We show that a small but significant orbital eccentricity is required to match post-Newtonian and quasiequilibrium calculations. If this proves to be a real eccentricity, it could affect the fine details of the subsequent numerical evolutions and the predicted gravitational waveforms.

gr-qc↗

arXiv2006

Supermassive black holes or boson stars? Hair counting with gravitational wave detectors

The evidence for supermassive Kerr black holes in galactic centers is strong and growing, but only the detection of gravitational waves will convincingly rule out other possibilities to explain the observations. The Kerr spacetime is completely specified by the first two multipole moments: mass and angular momentum. This is usually referred to as the ``no-hair theorem'', but it is really a ``two-hair'' theorem. If general relativity is the correct theory of gravity, the most plausible alternative to a supermassive Kerr black hole is a rotating boson star. Numerical calculations indicate that the spacetime of rotating boson stars is determined by the first three multipole moments (``three-hair theorem''). LISA could accurately measure the oscillation frequencies of these supermassive objects. We propose to use these measurements to ``count their hair'', unambiguously determining their nature and properties.

gr-qc↗

arXiv2006

LISA observations of massive black hole mergers: event rates and issues in waveform modelling

The observability of gravitational waves from supermassive and intermediate-mass black holes by the forecoming Laser Interferometer Space Antenna (LISA), and the physics we can learn from the observations, will depend on two basic factors: the event rates for massive black hole mergers occurring in the LISA best sensitivity window, and our theoretical knowledge of the gravitational waveforms. We first provide a concise review of the literature on LISA event rates for massive black hole mergers, as predicted by different formation scenarios. Then we discuss what (in our view) are the most urgent issues to address in terms of waveform modelling. For massive black hole binary inspiral these include spin precession, eccentricity, the effect of high-order Post-Newtonian terms in the amplitude and phase, and an accurate prediction of the transition from inspiral to plunge. For black hole ringdown, numerical relativity will ultimately be required to determine the relative quasinormal mode excitation, and to reduce the dimensionality of the template space in matched filtering.

astro-ph↗

arXiv2006

Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions

Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher dimensions, quantum field theory in curved space-time and studies of D-branes. We first review analytic and numerical calculations of their eigenvalues and eigenfunctions in four dimensions, filling gaps in the existing literature when necessary. Then we compute the angular dependence of the spin-weighted spheroidal harmonics corresponding to slowly-damped quasinormal mode frequencies of the Kerr black hole, providing numerical tables and approximate formulas for their scalar products. Finally we present an exhaustive analytic and numerical study of scalar spheroidal harmonics in (n+4) dimensions.

gr-qc↗

arXiv2006

On 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 quasi-normal 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 multi-mode 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.

gr-qc↗

arXiv2006

Considerations on the excitation of black hole quasinormal modes

We provide some considerations on the excitation of black hole quasinormal modes (QNMs) in different physical scenarios. Considering a simple model in which a stream of particles accretes onto a black hole, we show that resonant QNM excitation by hyperaccretion requires a significant amount of fine-tuning, and is quite unlikely to occur in nature. Then we summarize and discuss present estimates of black hole QNM excitation from gravitational collapse, distorted black holes and head-on black hole collisions. We emphasize the areas that, in our opinion, are in urgent need of further investigation from the point of view of gravitational wave source modeling.

gr-qc↗

arXiv2005

Testing general relativity and probing the merger history of massive black holes with LISA

Observations of binary inspirals with LISA will allow us to place bounds on alternative theories of gravity and to study the merger history of massive black holes (MBH). These possibilities rely on LISA's parameter estimation accuracy. We update previous studies of parameter estimation including non-precessional spin effects. We work both in Einstein's theory and in alternative theories of gravity of the scalar-tensor and massive-graviton types. Inclusion of non-precessional spin terms in MBH binaries has little effect on the angular resolution or on distance determination accuracy, but it degrades the estimation of the chirp mass and reduced mass by between one and two orders of magnitude. The bound on the coupling parameter of scalar-tensor gravity is significantly reduced by the presence of spin couplings, while the reduction in the graviton-mass bound is milder. LISA will measure the luminosity distance of MBHs to better than ~10% out to z~4 for a (10^6+10^6) Msun binary, and out to z~2 for a (10^7+10^7) Msun binary. The chirp mass of a MBH binary can always be determined with excellent accuracy. Ignoring spin effects, the reduced mass can be measured within ~1% out to z=10 and beyond for a (10^6+10^6) Msun binary, but only out to z~2 for a (10^7+10^7) Msun binary. Present-day MBH coalescence rate calculations indicate that most detectable events should originate at z~2-6: at these redshifts LISA can be used to measure the two black hole masses and their luminosity distance with sufficient accuracy to probe the merger history of MBHs. If the low-frequency LISA noise can only be trusted down to 10^-4 Hz, parameter estimation for MBHs (and LISA's ability to perform reliable cosmological observations) will be significantly degraded.

gr-qc↗

arXiv2005

What we (don't) know about black hole formation in high-energy collisions

Higher-dimensional scenarios allow for the formation of mini-black holes from TeV-scale particle collisions. The purpose of this paper is to review and compare different methods for the estimate of the total gravitational energy emitted in this process. To date, black hole formation has mainly been studied using an apparent horizon search technique. This approach yields only an upper bound on the gravitational energy emitted during black hole formation. Alternative calculations based on instantaneous collisions of point particles and black hole perturbation theory suggest that the emitted gravitational energy may be smaller. New and more refined methods may be necessary to accurately describe black hole formation in high-energy particle collisions.

hep-ph↗

arXiv2005

Quasinormal modes of Kerr-Newman black holes: coupling of electromagnetic and gravitational perturbations

We compute numerically the quasinormal modes of Kerr-Newman black holes in the scalar case, for which the perturbation equations are separable. Then we study different approximations to decouple electromagnetic and gravitational perturbations of the Kerr-Newman metric, computing the corresponding quasinormal modes. Our results suggest that the Teukolsky-like equation derived by Dudley and Finley gives a good approximation to the dynamics of a rotating charged black hole for Q<M/2. Though insufficient to deal with Kerr-Newman based models of elementary particles, the Dudley-Finley equation should be adequate for astrophysical applications.

gr-qc↗

arXiv2005

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 omega_BD 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 black-hole 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.

gr-qc↗

arXiv2005

Rotating neutron stars: an invariant comparison of approximate and numerical spacetime models

We compare three different models of rotating neutron star spacetimes: the Hartle-Thorne (HT) slow-rotation approximation at second order in rotation, the exact analytic vacuum solution of Manko et al. and a numerical solution of the full Einstein equations. We integrate the HT structure equations for five representative equations of state. Then we match the HT models to numerical solutions of the Einstein equations, imposing that the mass and angular momentum of the models be the same. We estimate the limits of validity of the HT expansion computing relative errors in the spacetime's quadrupole moment Q and in the ISCO radii. We find that ISCO radii computed in the HT approximation are accurate to better than 1%, even for the fastest observed ms pulsar. At the same rotational rates the accuracy on Q is of order 20%. In the second part of the paper we focus on the exterior vacuum spacetimes. We introduce a physically motivated `quasi-Kinnersley' Newman-Penrose frame. In this frame we evaluate the speciality index S, a coordinate-independent quantity measuring the deviation of each model from Petrov Type D. On the equatorial plane this deviation is smaller than 5%, even for the fastest rotating models. Our main conclusion is that the HT approximation is very reliable for most astrophysical applications.

gr-qc↗

arXiv2004

Quasinormal modes and classical wave propagation in analogue black holes

Many properties of black holes can be studied using acoustic analogues in the laboratory through the propagation of sound waves. We investigate in detail sound wave propagation in a rotating acoustic (2+1)-dimensional black hole, which corresponds to the ``draining bathtub'' fluid flow. We compute the quasinormal mode frequencies of this system and discuss late-time power-law tails. Due to the presence of an ergoregion, waves in a rotating acoustic black hole can be superradiantly amplified. We compute superradiant reflection coefficients and instability timescales for the acoustic black hole bomb, the equivalent of the Press-Teukolsky black hole bomb. Finally we discuss quasinormal modes and late-time tails in a non-rotating canonical acoustic black hole, corresponding to an incompressible, spherically symmetric (3+1)-dimensional fluid flow.

gr-qc↗

arXiv2004

Black hole quasinormal modes: hints of quantum gravity?

This is a short review of the quasinormal mode spectrum of Schwarzschild, Reissner-Nordstrom and Kerr black holes. The summary includes previously unpublished calculations of i) the eigenvalues of spin-weighted spheroidal harmonics, and ii) quasinormal frequencies of extremal Reissner-Nordstrom black holes.

gr-qc↗

arXiv2004

Gravitational energy loss in high energy particle collisions: ultrarelativistic plunge into a multidimensional black hole

We investigate the gravitational energy emission of an ultrarelativistic particle radially falling into a D-dimensional black hole. We numerically integrate the equations describing black hole gravitational perturbations and obtain energy spectra, total energy and angular distribution of the emitted gravitational radiation. The black hole quasinormal modes for scalar, vector, and tensor perturbations are computed in the WKB approximation. We discuss our results in the context of black hole production at the TeV scale.

hep-th↗