Momentum flow in black-hole binaries. I. Post-Newtonian analysis of the inspiral and spin-induced bobbing

Abstract

A brief overview is presented of a new Caltech/Cornell research program that is exploring the nonlinear dynamics of curved spacetime in binary black hole collisions and mergers, and of an initial project in this program aimed at elucidating the flow of linear momentum in black-hole binaries (BBHs). The "gauge-dependence" (arbitrariness) in the localization of linear momentum in BBHs is discussed, along with the hope that the qualitative behavior of linear momentum will be gaugeindependent. Harmonic coordinates are suggested as a possibly preferred foundation for fixing the gauge associated with linear momentum. For a BBH or other compact binary, the LandauLifshitz formalism is used to define the momenta of the binary's individual bodies in terms of integrals over the bodies' surfaces or interiors, and define the momentum of the gravitational field (spacetime curvature) outside the bodies as a volume integral over the field's momentum density. These definitions will be used in subsequent papers that explore the internal nonlinear dynamics of BBHs via numerical relativity. This formalism is then used, in the 1.5PN approximation, to explore momentum flow between a binary's bodies and its gravitational field during the binary's orbital inspiral. Special attention is paid to momentum flow and conservation associated with synchronous spin-induced bobbing of the black holes, in the so-called "extreme-kick configuration" (where two identical black holes have their spins lying in their orbital plane and antialigned).

Superkicks in ultrarelativistic encounters of spinning black holes

“…The former has been studied, for example, in Refs. [7,8], and reveals substantial reversals (of order 10 3 km/s) in local estimates of the BH velocities. These large variations are not mirrored in the radiated linear momentum as measured far away from the BHs 2 , and henceforth, with "anti-kick" we exclusively refer to the deceleration visible in P rad as measured far away from the BHs.…”

Event horizon deformations in extreme mass-ratio black hole mergers

“…Since we are interested in the deformation of the future event horizon, we specialize the relations (3)(4)(5)(6)(7)(8) to the event horizon, where (r − 2) → 0 and Z and Q are functions of v ≡ t + r * alone:…”

“…The most immediately relevant results are the gravitational waveforms emitted by such mergers, since accurate theoretical templates for these waveforms are crucial for their first detection [5]. As a further step, however, studying features of spacetime geometry in the strong-field region, as well as their possible connection with out-going gravitational waves, will facilitate the use of gravitational waves as a tool for studying the non-linear and highly dynamical regime of geometrodynamics [6][7][8][9].…”

The close-limit approximation for black hole binaries with post-Newtonian initial conditions

“…[16] for a recent example). Of particular importance is the close-limit (CL) approximation method, pioneered by Price & Pullin [17] and Abrahams & Price [18].…”