An explicit harmonic code for black-hole evolution using excision

Abstract

We describe an explicit in time, finite-difference code designed to simulate black holes by using the excision method. The code is based upon the harmonic formulation of the Einstein equations and incorporates several features regarding the well-posedness and numerical stability of the initialboundary problem for the quasilinear wave equation. After a discussion of the equations solved and of the techniques employed, we present a series of testbeds carried out to validate the code. Such tests range from the evolution of isolated black holes to the head-on collision of two black holes and then to a binary black hole inspiral and merger. Besides assessing the accuracy of the code, the inspiral and merger test has revealed that the marginally trapped surfaces contained within the common apparent horizon of the merged black hole can touch and even intersect. This novel feature in the dynamics of the marginally trapped surfaces is unexpected but consistent with theorems on the properties of these surfaces.

Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis

“…Thanks to a series of recent breakthroughs, long term evolutions of inspiralling binary black holes that last for more than one orbit have been obtained with several independent codes, and accurate gravitational wave signals have been computed [1,2,3,4,5,6,7,8,9,10,11].…”

Measuring orbital eccentricity and periastron advance in quasicircular black hole simulations

“…The late stage of the inspiral, corresponding to the final few orbits and merger of the binary, is highly dynamical and involves strong gravitational fields, and it must be handled by numerical relativity. Breakthroughs in numerical relativity have allowed a system of two inspiraling black holes to be evolved through merger and the ringdown of the remnant black hole [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Simulating binary neutron stars: Dynamics and gravitational waves

“…In relation to these efforts, and beyond the intrinsic importance of the two-body problem in general relativity (GR), it is significant that recent studies of the binary black hole problem have made substantial progress in providing waveforms for these mergers (see for instance [3,4,5,6,7,8]). Furthermore, these numerical results for vacuum spacetimes show a remarkable agreement with those obtained with approximation techniques [9,10].…”