The Close-Limit Approximation for Black Hole Binaries with Post-Newtonian Initial Conditions

Abstract

The ringdown phase of a black hole formed from the merger of two orbiting black holes is described by means of the close-limit (CL) approximation starting from second-post-Newtonian (2PN) initial conditions. The 2PN metric of point-particle binaries is formally expanded in CL form and identified with that of a perturbed Schwarzschild black hole. The multipolar coefficients describing the even-parity (polar) and odd-parity (axial) components of the linear perturbation consistently satisfy the 2PN-accurate perturbative field equations. We use these coefficients to build initial conditions for the Regge-Wheeler and Zerilli wave equations, which we then evolve numerically. The ringdown waveform is obtained in two cases: head-on collision with zero-angular momentum, composed only of even modes, and circular orbits, for which both even and odd modes contribute. In a separate work, this formalism is applied to the study of the gravitational recoil produced during the ringdown phase of coalescing binary black holes.

34 pages, 6 figures; to appear in Class. Quant. Grav

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Cited by in corpus (13)

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• Quasinormal modes and their excitation beyond general relativity
• Gravitational-wave echoes from numerical-relativity waveforms via space-time construction near merging compact objects
• The Status of Black-Hole Binary Merger Simulations with Numerical Relativity
• Hybrid method for understanding black-hole mergers: Inspiralling case
• A hybrid method for understanding black-hole mergers: head-on case
• Fundamental Tone and Overtones of Quasinormal Modes in Ringdown Gravitational Waves: A Detailed Study in Black Hole Perturbation
• Applications of the close-limit approximation: horizonless compact objects and scalar fields
• Eccentric Pairs: Analytic Gravitational Waves from Binary Black Holes in Elliptic Orbits
• Challenging theories of gravitation: dark matter, compact objects and gravitational waves