High-energy collision of two black holes

We study the head-on collision of two highly boosted equal mass, nonrotating black holes. We determine the waveforms, radiated energies, and mode excitation in the center of mass frame for a variety of boosts. For the first time we are able to compare analytic calculations, black-hole perturbation theory, and strong field, nonlinear numerical calculations for this problem. Extrapolation of our results, which include velocities of up to 0.94c, indicate that in the ultrarelativistic regime about 14+/-3% of the energy is converted into gravitational waves. This gives rise to a luminosity of order 10_(-2)c_(5)/G, the largest known so far in a black-hole merger.     

Initial data for two Kerr-like black holes

We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in an arbitrary location and with spins pointing in arbitrary directions. We also provide a method to compute them. If the mass parameter of one of the black holes is zero, then this family reduces exactly to the Kerr initial data. The existence proof is based on a general property of the Kerr metric which can be used in other constructions as well. Further generalizations are also discussed.     

Gravitational field in a collision of two Schwarzschild black holes

This paper presents an analysis of the linearized Einstein equations in vacuum for the problem of head-on collision of two Schwarzschild black holes, of which one is much smaller than the other. Based on the decomposition of the metric perturbations into spherical harmonics, introduced by Regge and Wheeler, we give some time-symmetric initial data and calculate the subsequent time-evolution of gravitational field. It is found that the small hole, initially at rest, begins to move like a freely falling particle. A wave-like disturbance generated near the small hole grows up and propagates in the direction opposite to the hole's motion. We investigate the area of the large Schwarzschild horizon distorted by the small hole to obtain the rate of increase with time.     

RIO: a new computational framework for accurate initial data of binary black holes

We present a computational framework (Rio) in the ADM 3+1 approach for numerical relativity. This work enables us to carry out high resolution calculations for initial data of two arbitrary black holes. We use the transverse conformal treatment, the Bowen–York and the puncture methods. For the numerical solution of the Hamiltonian constraint we use the domain decomposition and the spectral decomposition of Galerkin–Collocation. The nonlinear numerical code solves the set of equations for the spectral modes using the standard Newton–Raphson method, LU decomposition and Gaussian quadratures. We show the convergence of the Rio code. This code allows for easy deployment of large calculations. We show how the spin of one of the black holes is manifest in the conformal factor.     

The time symmetric initial value problem for black holes

The time symmetric initial value problem for black holes is discussed. It is shown that if a solution contains marginally trapped surfaces these correspond to minimal surfaces lying inside the black holes. Such minimal surfaces must have spherical topology. These minimal surfaces are used to obtain lower bounds for the areas of event horizons and upper bounds for the efficiency for radiating gravitational radiation. It is shown that moving black holes closer together reduces the energy available and that a single initially distorted black hole (perhaps formed just after a very assymetric collapse) cannot radiate more than 65% of its rest mass away. Wormholes are also briefly discussed.     

Apparent horizons of time-symmetric initial value for three black holes

The apparent horizon of three black holes on a time-symmetric space-like hypersurface is examined. The area is computed for various values of separation parameters. Using Hawking's mass formula, we found that the maximum possible efficiency of energy release is no more than 8.44 × 10^-3 when the initial apparent horizon encloses three black holes.     

Initial data for black holes and black strings in 5D

We explore time-symmetric hypersurfaces containing apparent horizons of black objects in a 5D spacetime with one coordinate compactified on a circle. We find a phase transition within the family of such hypersurfaces: the horizon has different topology for different parameters. The topology varies from S3 to S2 x S1. This phase transition is discontinuous--the topology of the horizon changes abruptly. We explore the behavior around the critical point and present a possible phase diagram.     

Multipole analysis of kicks in collision of spinning binary black holes

Thorne and Kidder give expressions which allow for analytical estimates of the “kick”, i.e. the recoil, produced from asymmetrical gravitational radiation during the interaction of black holes, or in fact any gravitating compact bodies. (The Thorne-Kidder formula uses momentum flux calculations based on the linearized General Relativity of gravitational radiation). We specifically treat kicks arising in the binary interaction of equal mass black holes, when at least one of the black holes has significant spin, a. Such configurations can produce very large kicks in computational simulations. We consider both fly-by and quasicircular orbits. For fly-by orbits we find substantial kicks from those Thorne-Kidder terms which are linear in a. For the quasi-circular case, we consider in addition the nonlinear contribution (O(a ²)) to the kicks, and provide a dynamical explanation for such terms discovered and displayed by [2]. However, in the cases of maximal kick velocities, the dependence on spin is largely linear (reproduced in numerical results [6]).     

Collision of two rotating Hayward black holes

We investigate the spin interaction and the gravitational radiation thermally allowed in a head-on collision of two rotating Hayward black holes. The Hayward black hole is a regular black hole in a modified Einstein equation, and hence it can be an appropriate model to describe the extent to which the regularity effect in the near-horizon region affects the interaction and the radiation. If one black hole is assumed to be considerably smaller than the other, the potential of the spin interaction can be analytically obtained and is dependent on the alignment of angular momenta of the black holes. For the collision of massive black holes, the gravitational radiation is numerically obtained as the upper bound by using the laws of thermodynamics. The effect of the Hayward black hole tends to increase the radiation energy, but we can limit the effect by comparing the radiation energy with the gravitational waves GW150914 and GW151226.     

The horizons of two Schwarzschild black holes

The problem investigated is that of two Schwarzschild black holes of massesm ₁ andm ₂m ₁, which are initially at rest on a time-symmetric spacelike hypersurface. An asymptotic formula asm ₂0 is found for the maximum separation betweenm ₁ andm ₂ such that a connected component of the apparent horizon encloses bothm ₁ andm ₂. The problem is solved numerically.