Formulations of the Einstein equations for numerical simulations - General Relativity and Quantum CosmologyReportar como inadecuado




Formulations of the Einstein equations for numerical simulations - General Relativity and Quantum Cosmology - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We review recent efforts to re-formulate the Einstein equations for fullyrelativistic numerical simulations. In order to complete a long-term andaccurate simulations of binary compact objects, people seek a robust set ofequations against the violation of constraints. Many trials have revealed thatmathematically equivalent sets of evolution equations show different numericalstability in free evolution schemes. In this article, we overview the effortsof the community, categorizing them into three directions: 1 modifications ofthe standard Arnowitt-Deser-Misner equations initiated by the Kyoto group theso-called Baumgarte-Shapiro-Shibata-Nakamura equations, 2 rewriting theevolution equations in a hyperbolic form, and 3 construction of an-asymptotically constrained- system. We then introduce our series of works thattries to explain these evolution behaviors in a unified way using eigenvalueanalysis of the constraint propagation equations. The modifications of oradjustments to the evolution equations change the character of constraintpropagation, and several particular adjustments using constraints are expectedto damp the constraint-violating modes. We show several set of adjustedADM-BSSN equations, together with their numerical demonstrations.



Autor: Hisa-aki Shinkai

Fuente: https://arxiv.org/







Documentos relacionados