arXiv subjects

R. Gomez

Publications and source records attributed to R. Gomez.

22 records · Page 2Linked to original sources

arXiv1997

Gravitational wave extraction and outer boundary conditions by perturbative matching

We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code.

gr-qc↗

arXiv1997

Black hole excision with matching

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 code, for the spherically symmetric collapse of a self-gravitating scalar field, shows that matching performs at least as well as other approaches to handling the inner boundary.

gr-qc↗

arXiv1997

Cauchy-characteristic extraction in numerical relativity

We treat the calculation of gravitational radiation using the mixed timelike-null initial value formulation of general relativity. The determination of an exterior radiative solution is based on boundary values on a timelike worldtube $Γ$ and on characteristic data on an outgoing null cone emanating from an initial cross-section of $Γ$. We present the details of a 3-dimensional computational algorithm which evolves this initial data on a numerical grid, which is compactified to include future null infinity as finite grid points. A code implementing this algorithm is calibrated in the quasispherical regime. We consider the application of this procedure to the extraction of waveforms at infinity from an interior Cauchy evolution, which provides the boundary data on $Γ$. This is a first step towards Cauchy-characteristic matching in which the data flow at the boundary $Γ$ is two-way, with the Cauchy and characteristic computations providing exact boundary values for each other. We describe strategies for implementing matching and show that for small target error it is much more computationally efficient than alternative methods.

gr-qc↗

arXiv1997

The eth formalism in numerical relativity

We present a finite difference version of the eth formalism, which allows use of tensor fields in spherical coordinates in a manner which avoids polar singularities. The method employs two overlapping stereographic coordinate patches, with interpolations between the patches in the regions of overlap. It provides a new and effective computational tool for dealing with a wide variety of systems in which spherical coordinates are natural, such as the generation of radiation from an isolated source. We test the formalism with the evolution of waves in three spatial dimensions and the calculation of the curvature scalar of arbitrarily curved geometries on topologically spherical manifolds. The formalism is applied to the solution of the Robinson-Trautman equation and reveals some new features of gravitational waveforms in the nonlinear regime.

gr-qc↗