Related papers: A Multiple-Grid-Patch Evolution Scheme for 3-D Bla…
We use rigorous techniques from numerical analysis of hyperbolic equations in bounded domains to construct stable finite-difference schemes for Numerical Relativity, in particular for their use in black hole excision. As an application, we…
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…
A new numerical method is introduced to study the problem of time evolution of generic non-linear dynamical systems in four-dimensional spacetimes. It is assumed that the time level surfaces are foliated by a one-parameter family of…
We experiment with modifications of the BSSN form of the Einstein field equations (a reformulation of the ADM equations) and demonstrate how these modifications affect the stability of numerical black hole evolution calculations. We use…
We present a new method for treating the inner Cauchy boundary of a black hole spacetime by matching to a characteristic evolution. We discuss the advantages and disadvantages of such a scheme relative to Cauchy-only approaches. A prototype…
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…
We present the first results for Cauchy nonlinear evolution of 3D, nonaxisymmetric distorted black holes. We focus on the extraction and verification of 3D waveforms determined by numerical relativity. We show that the black hole evolution…
We present an algorithm for treating mesh refinement interfaces in numerical relativity. We detail the behavior of the solution near such interfaces located in the strong field regions of dynamical black hole spacetimes, with particular…
This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further…
Numerical codes based on a direct implementation of the standard ADM formulation of Einstein's equations have generally failed to provide long-term stable and convergent evolutions of black hole spacetimes when excision is used to remove…
We present a new warped gridding scheme adapted to simulating gas dynamics in binary black hole spacetimes. The grid concentrates grid points in the vicinity of each black hole to resolve the smaller scale structures there, and rarefies…
Fallback supernovae and the collapsar scenario for long-gamma ray burst and hypernovae have received considerable interest as pathways to black-hole formation and extreme transient events. Consistent simulations of these scenarios require a…
We have developed a numerical code to study the evolution of self-gravitating matter in dynamic black hole axisymmetric spacetimes in general relativity. The matter fields are evolved with a high-resolution shock-capturing scheme that uses…
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…
We propose a novel ansatz, where the full black hole geometry is written as a linear in mass perturbation of the associated extremal black hole base. Contrary to its "standard" version, the corresponding "extremal Kerr-Schild form" is no…
We present a numerical work aiming at the computation of excised initial data for black hole spacetimes in full general relativity, using Dirac gauge in the context of a constrained formalism for the Einstein equations. Introducing the…
We consider a series of distorted black hole initial data sets, and develop techniques to evolve them using the linearized equations of motion for the gravitational wave perturbations on a Schwarzschild background. We apply this to 2D and…
We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used,…
Black holes accreting well below the Eddington rate are believed to have geometrically thick, optically thin, rotationally supported accretion discs in which the Coulomb mean free path is large compared to $GM/c^2$. In such an environment,…
We present a simple method for applying excision boundary conditions for the relativistic Euler equations. This method depends on the use of Reconstruction-Evolution methods, a standard class of HRSC methods. We test three different…