Gravitational waves from binary black holes in the extreme mass ratio regime: self-force calculations (original) (raw)
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Physical Review D
We compare recently computed waveforms from second-order gravitational self-force (GSF) theory to those generated by a new, GSF-informed, effective one body (EOB) waveform model for (spinaligned, eccentric) inspiralling black hole binaries with large mass ratios. We focus on quasi-circular, nonspinning, configurations and perform detailed GSF/EOB waveform phasing comparisons, either in the time domain or via the gauge-invariant dimensionless function Qω ≡ ω 2 /ω, where ω is the gravitational wave frequency. The inclusion of high-PN test-mass terms within the EOB radiation reaction (notably, up to 22PN) is crucial to achieve an EOB/GSF phasing agreement below 1 rad up to the end of the inspiral for mass ratios up to 500. For larger mass ratios, up to 5 × 10 4 , the contribution of horizon absorption becomes more and more important and needs to be accurately modeled. Our results indicate that our GSF-informed EOB waveform model is a promising tool to describe waveforms generated by either intermediate or extreme mass ratio inspirals for future gravitational wave detectors.
Physical Review D, 2006
The description of extreme-mass-ratio binary systems in the inspiral phase is a challenging problem in gravitational wave physics with significant relevance for the space interferometer LISA. The main difficulty lies in the evaluation of the effects of the small body's gravitational field on itself. To that end, an accurate computation of the perturbations produced by the small body with respect the background geometry of the large object, a massive black hole, is required. In this paper we present a new computational approach based on Finite Element Methods to solve the master equations describing perturbations of non-rotating black holes due to an orbiting point-like object. The numerical computations are carried out in the time domain by using evolution algorithms for wave-type equations. We show the accuracy of the method by comparing our calculations with previous results in the literature. Finally, we discuss the relevance of this method for achieving accurate descriptions of extreme-mass-ratio binaries.
Analytic Black Hole Perturbation Approach to Gravitational Radiation
Living Reviews in Relativity, 2003
We review the analytic methods used to perform the post-Newtonian expansion of gravitational waves induced by a particle orbiting a massive, compact body, based on black hole perturbation theory. There exist two different methods of performing the post-Newtonian expansion. Both are based on the Teukolsky equation. In one method, the Teukolsky equation is transformed into a Regge-Wheeler type equation that reduces to the standard Klein-Gordon equation in the flat-space limit, while in the other method (which was introduced by Mano, Suzuki, and Takasugi relatively recently), the Teukolsky equation is used directly in its original form. The former's advantage is that it is intuitively easy to understand how various curved space effects come into play. However, it becomes increasingly complicated when one 16 2 − 243 8 − 785 6)︀ 5 .
Physical Review D, 1996
We derive the gravitational waveform and gravitational-wave energy flux generated by a binary star system of compact objects (neutron stars or black holes), accurate through second post-Newtonian order (O[(v/c) 4 ] ∼ O[(Gm/rc 2) 2 ]) beyond the lowest-order quadrupole approximation. We cast the Einstein equations into the form of a flat-spacetime wave equation together with a harmonic gauge condition, and solve it formally as a retarded integral over the past null cone of the chosen field point. The part of this integral that involves the matter sources and the near-zone gravitational field is evaluated in terms of multipole moments using standard techniques; the remainder of the retarded integral, extending over the radiation zone, is evaluated in a novel way. The result is a manifestly convergent and finite procedure for calculating gravitational radiation to arbitrary orders in a post-Newtonian expansion. Through second post-Newtonian order, the radiation is also shown to propagate toward the observer along true null rays of the asymptotically Schwarzschild spacetime, despite having been derived using flat spacetime wave equations. The method cures defects that plagued previous "brute-force" slow-motion approaches to the generation of gravitational radiation, and yields results that agree perfectly with those recently obtained by a mixed post-Minkowskian post-Newtonian method. We display explicit formulae for the gravitational waveform and the energy flux for two-body systems, both in arbitrary orbits and in circular orbits. In an appendix, we extend the formalism to bodies with finite spatial extent, and derive the spin corrections to the waveform and energy loss.
Classical and Quantum Gravity, 2006
Comparing the corrections to Kepler's law with orbital evolution under a self force, we extract the finite, already regularized part of the latter in a specific gauge. We apply this method to a quasicircular orbit around a Schwarzschild black hole of an extreme mass ratio binary, and determine the first-and second-order conservative gravitational self force in a post Newtonian expansion. We use these results in the construction of the gravitational waveform, and revisit the question of the relative contribution of the self force and spin-orbit coupling.
Classical and Quantum Gravity, 2001
Here we present the results of applying the generalized Riemann ζ-function regularization method to the gravitational radiation reaction problem. We analyse in detail the head-on collision of two non-spinning black holes with an extreme mass ratio. The resulting reaction force on the smaller hole is repulsive. We discuss the possible extensions of these method to generic orbits and spinning black holes. The determination of corrected trajectories allows us to add second perturbative corrections with the consequent increase in the accuracy of computed waveforms.
We present the orbit-integrated self force effects on the gravitational waveform for an IMRI source. We consider the quasi-circular motion of a particle in the spacetime of a Schwarzschild black hole and study the dependence of the dephasing of the corresponding gravitational waveforms due to ignoring the conservative piece of the self force or the second order dissipative piece of the self force. First order self forces are modeled by the fully relativistic Barack--Sago self force. Second order effects are approximated by their post Newtonian expressions. This hybrid approach allows us to gain insight into the quantitative aspects of second order self-force effects, although the post Newtonian approximation of the second order effect does not allow us to quantitatively determine the observable quantities of interest. However, when fully relativistic second order effects become known, out method will allow us to refine our analysis by including them. We calculate the cumulative deph...
Physical Review D, 2014
The post-Newtonian approximation is still the most widely used approach to obtaining explicit solutions in general relativity, especially for the relativistic two-body problem with arbitrary mass ratio. Within many of its applications, it is often required to use a regularization procedure. Though frequently misunderstood, the regularization is essential for waveform generation without reference to the internal structure of orbiting bodies. In recent years, direct comparison with the self-force approach, constructed specifically for highly relativistic particles in the extreme mass ratio limit, has enabled preliminary confirmation of the foundations of both computational methods, including their very independent regularization procedures, with high numerical precision. In this paper, we build upon earlier work to carry this comparison still further, by examining next-to-nextto-leading order contributions beyond the half integral 5.5PN conservative effect, which arise from terms to cubic and higher orders in the metric and its multipole moments, thus extending scrutiny of the post-Newtonian methods to one of the highest orders yet achieved. We do this by explicitly constructing tail-of-tail terms at 6.5PN and 7.5PN order, computing the redshift factor for compact binaries in the small mass ratio limit, and comparing directly with numerically and analytically computed terms in the self-force approach, obtained using solutions for metric perturbations in the Schwarzschild space-time, and a combination of exact series representations possibly with more typical PN expansions. While self force results may be relativistic but with restricted mass ratio, our methods, valid primarily in the weak-field slowly-moving regime, are nevertheless in principle applicable for arbitrary mass ratios.
Black Hole Perturbations: A Review of Recent Analytical Results
Foundations of Physics, 2018
We review the gravitational self-force program to analytically compute first-order metric perturbations in a Schwarzschild black hole spacetime in the case of a perturbing (small) mass moving on a slightly eccentric equatorial orbit. The perturbed metric components should then be combined into gauge-invariant quantities to be associated with physical observables. In this way, for example, one determines the various "potentials" entering the Effective-One-Body model, i.e., a powerful formalism for the description of the gravitational interaction of two masses, which is currently successfully used for the analysis of gravitational wave signals.