Momentum flow in black-hole binaries. II. Numerical simulations of equal-mass, head-on mergers with antiparallel spins

Abstract

Research on extracting science from binary-black-hole (BBH) simulations has often adopted a ''scattering matrix'' perspective: given the binary's initial parameters, what are the final hole's parameters and the emitted gravitational waveform? In contrast, we are using BBH simulations to explore the nonlinear dynamics of curved spacetime. Focusing on the head-on plunge, merger, and ringdown of a BBH with transverse, antiparallel spins, we explore numerically the momentum flow between the holes and the surrounding spacetime. We use the Landau-Lifshitz field-theory-in-flat-spacetime formulation of general relativity to define and compute the density of field energy and field momentum outside horizons and the energy and momentum contained within horizons, and we define the effective velocity of each apparent and event horizon as the ratio of its enclosed momentum to its enclosed mass-energy. We find surprisingly good agreement between the horizons' effective and coordinate velocities. During the plunge, the holes experience a frame-dragging-induced acceleration orthogonal to the plane of their spins and their infall (''downward''), and they reach downward speeds of order 1000 km=s. When the common apparent horizon forms (and when the event horizons merge and their merged neck expands), the horizon swallows upward field momentum that resided between the holes, causing the merged hole to accelerate in the opposite (''upward'') direction. As the merged hole and the field energy and momentum settle down, a pulsational burst of gravitational waves is emitted, and the merged hole has a final effective velocity of about 20 km=s upward, which agrees with the recoil velocity obtained by measuring the linear momentum carried to infinity by the emitted gravitational radiation. To investigate the gauge dependence of our results, we compare generalized harmonic and Baumgarte-Shapiro-Shibata-Nakamura-moving-puncture evolutions of physically similar initial data; although the generalized harmonic and Baumgarte-ShapiroShibata-Nakamura-moving-puncture simulations use different gauge conditions, we find remarkably good agreement for our results in these two cases. We also compare our simulations with the post-Newtonian trajectories and near-field energy-momentum.

Final remnant of binary black hole mergers: Multipolar analysis

“…The data used here are from the ringdown after the collision of two black holes of nonzero antialigned spin (and therefore zero total angular momentum) starting from rest. This is a simple test case that can be used for studying black hole kicks, and the particular simulation studied here will be presented in great detail for that goal in an upcoming paper [45]. For the present purposes, the important points are that the final state is nonspinning, and that two orthogonal planes of reflection symmetry (the coordinate x = 0 and z = 0 planes, with the final kick being in the y direction) hold the harmonics in place, in that they remain symmetric or antisymmetric under the action of the reflection symmetries.…”

Radial infall of two compact objects: 2.5-post-Newtonian linear momentum flux and associated recoil

“…On the numerical relativity front, Anninos and Brandt [28] computed the recoil velocity due to head-on collision of two unequal mass black holes. Some other (relatively recent) analytical/numerical works [25,29,30] compute the recoil effects taking in to account the asymmetry in mass and/or in the spin. As far as PN calculations are concerned, although, the recoil effects in a head-on collision case have not been investigated explicitly, one can use expressions for the linear momentum flux from nonspinning inspiralling compact binary systems moving in general orbits [4,5,8] to write equivalent expressions for the head-on case by using the following transformations 1 (as suggested in [31,32]):…”

Geometrodynamics: the nonlinear dynamics of curved spacetime

“…Our first example is a simulation [22] of the head-on collision of two transversely spinning black holes, depicted in Fig. 9.…”