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arXiv · 0910.4593

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

Alexandre Le Tiec·Luc Blanchet
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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.

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Alexandre Le Tiec, Luc Blanchet. 2010-01-28. The Close-Limit Approximation for Black Hole Binaries with Post-Newtonian Initial Conditions. https://doi.org/10.1088/0264-9381%2F27%2F4%2F045008

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