Related papers: Toward computing gravitational initial data withou…
The Einstein constraint equations describe the space of initial data for the evolution equations, dictating how space should curve within spacetime. Under certain assumptions, the constraints reduce to a scalar quasilinear parabolic…
We describe an implicit general relativistic hydrodynamics code. The evolution equations are formulated in comoving coordinates. A conservative finite differencing of the Einstein equations is outlined, and artificial viscosity and…
We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously…
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…
We study the method for generating the initial data of black hole systems in Gauss-Bonnet (GB) gravity. The initial data are assumed to be momentarily static and conformally flat. Although the equation for the conformal factor is highly…
Gravitational wave astronomy has opened an unprecedented window onto tests of gravity and fundamental physics in the strong-field regime. In this study, we examine a series of well-motivated deviations from the classical Kerr solution of…
We present improvements to construction of binary black hole initial data used in SpEC (the Spectral Einstein Code). We introduce new boundary conditions for the extended conformal thin sandwich elliptic equations that enforce the excision…
A general method is presented for estimating the uncertainty in hybrid models of gravitational waveforms from binary black-hole systems with arbitrary physical parameters, and thence the highest allowable initial orbital frequency for a…
Eccentric black-hole binaries are among the most awaited sources of gravitational waves, yet their dynamics lack a consistent framework that provides a detailed and physically robust evolutionary description due to gauge issues. We present…
Standard puncture initial data have been widely used for numerical binary black hole evolutions despite their shortcomings, most notably the inherent lack of gravitational radiation at the initial time that is later followed by a burst of…
This work consists of two distinct parts. In the first part we present a new method for solving the initial value problem of general relativity. Given any spatial metric with a surface orthogonal Killing field and two freely specified…
This is the first of a series of papers describing a numerical implementation of the conformally rescaled Einstein equation, an implementation designed to calculate asymptotically flat spacetimes, especially spacetimes containing black…
In contrast to regular ordinary differential equations, the problem of accurately setting initial conditions just emerges in the context of differential-algebraic equations where the dynamic degree of freedom of the system is smaller than…
Isolated horizon conditions enforce the time invariance of both the intrinsic and the extrinsic geometry of a (quasilocal) black hole horizon. Nonexpanding horizons, only requiring the invariance of the intrinsic geometry, have been…
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…
GRTresna is a multigrid solver designed to solve the constraint equations for the initial data required in numerical relativity simulations. In particular, it is focussed on scenarios with fundamental fields around black holes and…
I describe the conformal method for constructing solutions of the hyperboloidal constraint equations as well as the conditions needed on the free data in order to have regularity up to boundary for the solutions to the constraint equations.…
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of General Relativity. The initial value problem then consists of specifying initial data for all relevant fields on one such a spatial hypersurface. These fields are the…
We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the…
The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article the present update provides additional information on numerical schemes…