Binary Black Hole Coalescence in Semi-Analytic Puncture Evolution

TL;DR

This paper introduces a semi-analytic method for modeling binary black hole coalescence using a novel Skeleton Hamiltonian approach, incorporating gravitational radiation effects and comparing phase evolution with numerical relativity.

Contribution

It presents a new semi-analytic puncture evolution method that integrates gravitational radiation reaction within a Hamiltonian framework for binary black holes.

Findings

First-order comparison shows phase differences with numerical relativity.

Modified reactive dynamics needed for better phase agreement.

Provides an estimate for gravitational waveforms from black hole mergers.

Abstract

Binary black-hole coalescence is treated semi-analytically by a novel approach. Our prescription employs the conservative Skeleton Hamiltonian that describes orbiting Brill-Lindquist wormholes (termed punctures in Numerical Relativity) within a waveless truncation to the Einstein field equations [G. Faye, P. Jaranowski and G. Sch\"afer, Phys. Rev. D {\bf 69}, 124029 (2004)]. We incorporate, in a transparent Hamiltonian way and in Burke-Thorne gauge structure, the effects of gravitational radiation reaction into the above Skeleton dynamics with the help of 3.5PN accurate angular momentum flux for compact binaries in quasi-circular orbits to obtain a Semi-Analytic Puncture Evolution to model merging black-hole binaries. With the help of the TaylorT4 approximant at 3.5PN order, we perform a {\it first-order} comparison between gravitational wave phase evolutions in Numerical Relativity and our approach for equal-mass binary black holes. This comparison reveals that a modified Skeletonian reactive dynamics that employs flexible parameters will be required to prevent the dephasing between our scheme and Numerical Relativity, similar to what is pursued in the Effective One Body approach. A rough estimate for the gravitational waveform associated with the binary black-hole coalescence in our approach is also provided.