Einstein's evolution equations as a system of balance laws
- 15 August 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 40 (4), 1022-1026
- https://doi.org/10.1103/physrevd.40.1022
Abstract
The evolution system in the space plus time (3+1) decomposition of Einstein's field equations is explicitly written as a system of balance laws. This is achieved by demanding that the time coordinate be harmonic (harmonic synchronization) and the space coordinate lines be normal to the constant-time hypersurfaces. No symmetry nor special form of the metric has been assumed, so that the equations may be used as a part of a three-dimensional numerical code for general relativity. The particular case of spherical symmetry is also considered and a numerical test of this case is provided by using a nonstandard form of the Schwarzschild line element.Keywords
This publication has 10 references indexed in Scilit:
- Harmonic synchronizations of spacetimePhysical Review D, 1988
- Mixed analytic-numerical solutions for a simple radiating systemGeneral Relativity and Gravitation, 1987
- General relativistic axisymmetric rotating systems: Coordinates and equationsPhysics Reports, 1983
- Hyperbolicity of the 3+1 system of Einstein equationsCommunications in Mathematical Physics, 1983
- General Relativistic Collapse of Axially Symmetric Stars Leading to the Formation of Rotating Black HolesProgress of Theoretical Physics, 1981
- Interacting gravitational shocks in vacuum plane-symmetric cosmologiesThe Astrophysical Journal, 1980
- Plane-symmetric cosmologiesThe Astrophysical Journal, 1979
- Time functions in numerical relativity: Marginally bound dust collapsePhysical Review D, 1979
- Kinematical conditions in the construction of spacetimePhysical Review D, 1978
- Hydrodynamic Calculations of General-Relativistic CollapsePhysical Review B, 1966