Related papers: Numerical Evolution of Black Holes with a Hyperbol…
We have recently constructed a numerical code that evolves a spherically symmetric spacetime using a hyperbolic formulation of Einstein's equations. For the case of a Schwarzschild black hole, this code works well at early times, but…
We present a new many-parameter family of hyperbolic representations of Einstein's equations, which we obtain by a straightforward generalization of previously known systems. We solve the resulting evolution equations numerically for a…
Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite…
We present a method for computing the evolution of a spacetime containing a massive particle and a black hole. The essential idea is that the gravitational field is evolved using full numerical relativity, with the particle generating a…
We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to…
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…
An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to…
A first order symmetric hyperbolic tetrad formulation of the Einstein equations developed by Estabrook and Wahlquist and put into a form suitable for numerical relativity by Buchman and Bardeen (the WEBB formulation) is adapted to explicit…
We present a new solution in Einstein's General Relativity representing a Schwarzschild black hole immersed in a rotating universe. Such a solution is constructed analytically by means of the last unexplored Lie point symmetry of the Ernst…
Motivated by the newest progress in geometric flows both in mathematics and physics, we apply the geometric evolution equation to study some black-hole problems. Our results show that, under certain conditions, the geometric evolution…
The BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation of the Einstein evolution equations is written in spherical symmetry. These equations can be used to address a number of technical and conceptual issues in numerical relativity in…
Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein's equations with the harmonic slicing condition is presented.…
We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing…
Combining deeper insight of Einstein's equations with sophisticated numerical techniques promises the ability to construct accurate numerical implementations of these equations. We illustrate this in two examples, the numerical evolution of…
We consider unconstrained evolution schemes for the hyperboloidal initial value problem in numerical relativity as a promising candidate for the optimally efficient numerical treatment of radiating compact objects. Here, spherical symmetry…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
We report on the successful numerical evolution of the compactified hyperboloidal initial value problem in general relativity using generalized harmonic gauge. We work in spherical symmetry, using a massless scalar field to drive dynamics.…
Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such…
The 3+1 Hamiltonian formulation in the gauge $D_tN=-K$ on the lapse function fixes the direction of time associated with the trace $K$ of the extrinsic curvature tensor. The Hamiltonian equations hereby become hyperbolic. We study this new…
Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They provide a regularization of the standard…