Gravitational waves from binary black holes in the extreme mass ratio regime: self-force calculations (original) (raw)
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.
Physical Review D, 2013
We consider the importance of the second-order dissipative self force for gravitational wave dephasing for an extreme or intermediate mass ratio system moving along a quasi-circular Schwarzschild orbit. For the first-order self force we use the fully relativistic force in the Lorenz gauge for eternally circular geodesics. The second-order self force is modeled by its 3.5 post Newtonian counterpart. We evolve the system using the osculating orbits method, and obtain the gravitational waveforms, whose phase includes all the terms-within our approximation (and using the self force along circular geodesics)-that are independent of the system's mass ratio. The partial dephasing due to the second-order dissipative self force is substantially smaller than that of the first-order conservative self force, although they are both at the same order in the mass ratio.
Gravitational Radiation Reaction
Progress of Theoretical Physics Supplement, 2006
We give a short personally-biased review on the recent progress in our understanding of gravitational radiation reaction acting on a point particle orbiting a black hole. The main motivation of this study is to obtain sufficiently precise gravitational waveforms from inspiraling binary compact stars with a large mass ratio. For this purpose, various new concepts and techniques have been developed to compute the orbital evolution taking into account the gravitational self-force. Combining these ideas with a few supplementary new ideas, we try to outline a path to our goal here. * ) This subsection largely owes to discussion with N. Sago. * * ) When we reconstruct the metric perturbation from a solution of the master variable within the source distribution, more delicate treatment is necessary. 29) Below we use the assumption of the factorized form of the tensor Green function. This assumption is not necessary if we follow the derivation given by Wald, 28) and actually this assumption itself is not correct. 29) * ) We would like to come back to this point in future publication. * * ) There is another way given by Amos Ori during post-Capra discussion meeting (2003, Kyoto), which does not rely on the presence of GODS. We give a brief explanation of his argument here
Physical Review D, 1995
A particle of mass µ moves on a circular orbit of a nonrotating black hole of mass M. Under the restrictions µ/M ≪ 1 and v ≪ 1, where v is the orbital velocity (in units in which c = 1), we consider the gravitational waves emitted by such a binary system. The framework is that of blackhole perturbation theory. We calculateĖ, the rate at which the gravitational waves remove energy from the system. The total energy loss is given byĖ =Ė ∞ +Ė H , whereĖ ∞ denotes that part of the gravitational-wave energy which is carried off to infinity, whileĖ H denotes the part which is absorbed by the black hole. We show that the black-hole absorption is a small effect:Ė H /Ė ≃ v 8. This is explained by the presence of a potential barrier in the vicinity of the black hole: Most of the waves propagating initially toward the black hole are reflected off the barrier; the black hole is therefore unable to absorb much. The black-hole absorption (and indeed any other effect resulting from imposing ingoing-wave boundary conditions at the event horizon) are sufficiently small to be irrelevant to the construction of matched filters for gravitational-wave measurements. To derive this result we extend the techniques previously developed by Poisson and Sasaki for integrating the Regge-Wheeler equation. The extension consists of an explicit consideration of the horizon boundary conditions, which were largely ignored in the previous work. Finally, we compare the wave generation formalism which derives from perturbation theory to the post-Newtonian formalism of Blanchet and Damour. Among other things we consider the corrections to the asymptotic gravitational-wave field which are due to wave-propagation (tail) effects. The results obtained using perturbation theory are identical to that of post-Newtonian theory.
The Gravitational Radiation Emitted by Two Quasi-Particles around a Schwarzschild Black Hole
Journal of Modern Physics, 2018
We model analytically a relativistic problem consisting of two quasi-particles each with mass m in close orbit around a static Schwarzschild black hole with mass M = 1 situated at the center of mass of the system. The angular momentum l of the system is taken to be 2. We model the mass density of the orbiting particles as a δ-function and we assume that there are no deformations. To model the system, we apply the second-order differential equation obtained elsewhere for a dynamic thin matter shell on a Schwarzschild background. As it is the case in this paper, the framework on which the equation was obtained is Bodi-Sachs. The only change in the equation is that now the quasi-normal mode parameter represents the particle's orbital frequency from which we are able to analytically compute the gravitational radiation emitted by the system at null infinity. We note that in a real astrophysical scenario the dynamics of the particles paths will be very dynamic and complicated and that the analytical methods used here will have to be developed further to accommodate that.