Regular second order perturbations of binary black holes: The extreme mass ratio regime
arXiv:0804.3824 · doi:10.1088/0264-9381/26/1/015007
Abstract
In order to derive the precise gravitational waveforms for extreme mass ratio inspirals (EMRI), we develop a formulation for the second order metric perturbations produced by a point particle moving in the Schwarzschild spacetime. The second order waveforms satisfy a wave equation with an effective source build up from products of the first order perturbations and its derivatives. We have explicitly regularized this source at the horizon and at spatial infinity. We show that the effective source does not contain squares of the Dirac's delta and that perturbations are regular at the particle location. We introduce an asymptotically flat gauge for the radiation fields and the mode to compute explicitly the (leading) second order waveforms in the headon collision case. This case represents the first completion of the radiation reaction program self-consistently.
28 pages, no figure
References in corpus (54)
- Evolution of Binary Black Hole Spacetimes
- Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
- Gravitational wave extraction from an inspiraling configuration of merging black holes
- Second-Order Cosmological Perturbations from Inflation
- Gravitational Radiation Reaction to a Particle Motion
- Large Merger Recoils and Spin Flips From Generic Black-Hole Binaries
- An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
- Maximum gravitational recoil
- Total recoil: the maximum kick from nonspinning black-hole binary inspiral
- Relativistic second-order perturbations of the Einstein-de Sitter Universe
- The motion of point particles in curved spacetime
- Spinning-black-hole binaries: The orbital hang up
- Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
- On the Back Reaction Problem for Gravitational Perturbations
- Binary black hole merger dynamics and waveforms
- A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
- Getting a kick out of numerical relativity
- Second order gauge invariant gravitational perturbations of a Kerr black hole
- Spin Flips and Precession in Black-Hole-Binary Mergers
- Calculating the gravitational self force in Schwarzschild spacetime
- Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
- Unequal Mass Binary Black Hole Plunges and Gravitational Recoil
- The last orbit of binary black holes
- Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --
- Gravitational self force on a particle in circular orbit around a Schwarzschild black hole
- Spin-orbit interactions in black-hole binaries
- Colliding black holes: how far can the close approximation go?
- Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation
- Second order perturbations of a Schwarzschild black hole
- Foundations of multiple black hole evolutions
- Head-on collisions of black holes: the particle limit
- Gravitational radiation from Schwarzschild black holes: the second order perturbation formalism
- Second Order Quasi-Normal Mode of the Schwarzschild Black Hole
- Low multipole contributions to the gravitational self-force
- Computing the gravitational self-force on a compact object plunging into a Schwarzschild black hole
- Pragmatic approach to gravitational radiation reaction in binary black holes
- Understanding initial data for black hole collisions
- Relativistic second-order perturbations of nonzero-Λflat cosmological models and CMB anisotropies
- Gauge Invariant Variables in Two-Parameter Nonlinear Perturbations
- Second and higher-order quasi-normal modes in binary black hole mergers
- Second-order gravitational self-force
- Gauge Problem in the Gravitational Self-Force I. Harmonic Gauge Approach in the Schwarzschild Background
- Understanding the fate of merging supermassive black holes
- High-order gauge-invariant perturbations of a spherical spacetime
- Close encounters of three black holes
- Three-body equations of motion in successive post-Newtonian approximations
- Construction of the second-order gravitational perturbations produced by a compact object
- A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit
- Gauge Problem in the Gravitational Self-Force II. First Post Newtonian Force under Regge-Wheeler Gauge
- Reconstruction of Black Hole Metric Perturbations from Weyl Curvature II: The Regge-Wheeler gauge
- Second order perturbations of a Schwarzschild black hole: inclusion of odd parity perturbations
- Modulation of the gravitational waveform by the effect of radiation reaction
- Regularization of the second-order gravitational perturbations produced by a compact object
- Regular second order perturbations of extreme mass ratio black hole binaries
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- Second Order Perturbations of Kerr Black Holes: Reconstruction of the Metric
- A complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole
- Non-linearities in the tidal Love numbers of black holes
- Motion of small bodies in general relativity: foundations and implementations of the self-force
- Perturbative effects of spinning black holes with applications to recoil velocities
- A source-free integration method for black hole perturbations and self-force computation: Radial fall
- Free fall and self-force: an historical perspective
- Fourth order indirect integration method for black hole perturbations: even modes