Extreme Mass-Ratio Binary Black Hole Merger: Characteristics of the Test-Particle Limit

Abstract

We study binary black hole mergers in the extreme mass-ratio limit. We determine the energy, angular momentum, and linear momentum of the post-merger, remnant black hole. Unlike previous works, we perform our analysis directly in the test-particle limit by solving the Regge-Wheeler-Zerilli wave equation with a source that moves along a geodesic. We rely on the fact that toward the merger, small mass-ratio binary systems follow a quasiuniversal geodesic trajectory. This formalism captures the final premerger stages of small mass-ratio binaries and thus provides a straightforward universal description in a region inaccessible to numerical relativity simulations. We present a general waveform template that may be used in the search for gravitational wave bursts from small and intermediate mass-ratio binary systems. Finally, this formalism gives a formal proof that the recoil velocity is quadratic in the symmetric mass ratio $\nu$. Specifically, the velocity is given by $V/c\approx 0.0467{\nu }^2$. This result is about $4\%$ larger than previously estimated. Most of this difference stems from the inclusion of higher multipoles in our calculation.

11 pages, 7 figures. Accepted for publication in Physical Review D

References in corpus (15)

• High-accuracy waveforms for binary black hole inspiral, merger, and ringdown
• Gravitational wave snapshots of generic extreme mass ratio inspirals
• Faithful Effective-One-Body waveforms of small-mass-ratio coalescing black-hole binaries
• Recoil velocities from equal-mass binary black-hole mergers: a systematic investigation of spin-orbit aligned configurations
• Gravitational Recoil during Binary Black Hole Coalescence using the Effective One Body Approach
• Binary black hole merger in the extreme mass ratio limit
• Orbital Evolution of Extreme-Mass-Ratio Black-Hole Binaries with Numerical Relativity
• Extreme Mass-Ratio Inspirals in the Effective-One-Body Approach: Quasi-Circular, Equatorial Orbits around a Spinning Black Hole
• A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime
• Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis
• Intermediate-mass-ratio black hole binaries: intertwining numerical and perturbative techniques
• Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms
• Binary black hole merger gravitational waves and recoil in the large mass ratio limit
• The antikick strikes back: recoil velocities for nearly-extremal binary black hole mergers in the test-mass limit
• Ballistic orbits in Schwarzschild space-time and gravitational waves from EMR binary mergers

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• Dynamics around supermassive black holes: Extreme mass-ratio inspirals as gravitational-wave sources