TL;DR
This paper reformulates the BSSN equations in spherical symmetry to improve numerical relativity simulations of Schwarzschild black holes, demonstrating effective puncture evolution with boundary conditions and finite difference methods.
Contribution
It presents a spherical symmetry version of the BSSN formulation with boundary conditions suitable for puncture evolution, enabling better tracking on Kruskal--Szekeres diagrams.
Findings
Successful puncture evolution of Schwarzschild black holes
Implementation of boundary conditions for stable evolution
Use of fourth-order finite difference methods
Abstract
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 the context of a single Schwarzschild black hole. One of the benefits of spherical symmetry is that the numerical grid points can be tracked on a Kruskal--Szekeres diagram. Boundary conditions suitable for puncture evolution of a Schwarzschild black hole are presented. Several results are shown for puncture evolution using a fourth--order finite difference implementation of the equations.
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Taxonomy
TopicsPulsars and Gravitational Waves Research · Astrophysical Phenomena and Observations · Black Holes and Theoretical Physics