Related papers: A double-domain spectral method for black hole exc…
Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to…
Shibata, Ury\=u and Friedman recently suggested a new decomposition of Einstein's equations that is useful for constructing initial data. In contrast to previous decompositions, the conformal metric is no longer treated as a…
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…
Traditional black-hole binary puncture initial data is conformally flat. This unphysical assumption is coupled with a lack of radiation signature from the binary's past life. As a result, waveforms extracted from evolutions of this data…
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…
Approximate solutions to the Einstein field equations are a valuable tool to investigate gravitational phenomena. An important aspect of any approximation is to investigate and quantify its regime of validity. We present a study that…
For an arbitrary strong, spherically symmetric super-horizon curvature perturbation, we present analytical solutions of the Einstein equations in terms of asymptotic expansion over the ratio of the Hubble radius to the length-scale of the…
We introduce a gravitational waveform inversion strategy that discovers mechanical models of binary black hole (BBH) systems. We show that only a single time series of (possibly noisy) waveform data is necessary to construct the equations…
The parabolic-hyperbolic form of the constraints is integrated numerically. The applied numerical stencil is $4^{th}$ order accurate (in the spatial directions) while 'time'-integration is made by using the method of lines with a $4^{th}$…
We present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo-spectral methods. This problem is split into two parts. The first step is the determination of a suitable…
An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric…
We present a singularity excision algorithm appropriate for numerical simulations of black holes moving throughout the computational domain. The method is an extension of the excision procedure previously used to obtain stable simulations…
We present an algorithm for calculating the complete data on an event horizon which constitute the necessary input for characteristic evolution of the exterior spacetime. We apply this algorithm to study the intrinsic and extrinsic geometry…
We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data…
We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal…
Second-order self-force calculations will be critical for modelling extreme-mass-ratio inspirals, and they are now known to have high accuracy even for binaries with mass ratios $\sim 1:10$. Many of the challenges facing these calculations…
Worldtube excision is a method of reducing computational burden in Numerical Relativity simulations of binary black holes in situations where there is a good analytical model of the geometry around (one or both of) the objects. Two such…
We use the Kerr-Schild type Teukolsky equation (horizon penetrating) to evolve binary black hole initial data as proposed by Bishop {\em et al.} in the close limit. Our results are in agreement with those recently obtained by Sarbach {\em…
We present a new pseudo-spectral code for the simulation of evolution systems that are second order in space. We test this code by evolving a non-linear scalar wave equation. These non-linear waves can be stably evolved using very simple…
This work introduces the Elliptica pseudo-spectral code for generating initial data of binary neutron star systems. Building upon the recent Elliptica code update, we can now construct initial data using not only piecewise polytropic…