New first-order formulation for the Einstein equations

Abstract

We derive a new first-order formulation for Einstein's equations which involves fewer unknowns than other first-order formulations that have been proposed. The new formulation is based on the 3+1 decomposition with arbitrary lapse and shift. In the reduction to first order form only 8 particular combinations of the 18 first derivatives of the spatial metric are introduced. In the case of linearization about Minkowski space, the new formulation consists of symmetric hyperbolic system in 14 unknowns, namely the components of the extrinsic curvature perturbation and the 8 new variables, from whose solution the metric perturbation can be computed by integration.

arXiv comment6 pages

References in corpus (3)

• Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations
• Fixing Einstein's equations
• First-order symmetric-hyperbolic Einstein equations with arbitrary fixed gauge

Cited by in corpus (4)

• Long term black hole evolution with the BSSN system by pseudospectral methods
• First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations
• Numerical stability of the AA evolution system compared to the ADM and BSSN systems
• Constraint Preserving Boundary Conditions for Hyperbolic Formulations of Einstein's Equations