Physics
Scientific paper
Nov 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004cqgra..21.5043b&link_type=abstract
Classical and Quantum Gravity, Volume 21, Issue 22, pp. 5043-5074 (2004).
Physics
10
Scientific paper
We propose a new, augmented formulation of the coupled Euler Einstein equations for perfect fluids on plane-symmetric Gowdy spacetimes. The unknowns of the augmented system are the density and velocity of the fluid and the first- and second-order spacetime derivatives of the metric. We solve the Riemann problem for the augmented system, allowing propagating discontinuities in both the fluid variables and the first- and second-order derivatives of the geometry coefficients. Our main result, based on Glimm's random choice scheme, is the existence of solutions with bounded total variation of the Euler Einstein equations, up to the first time where a blow-up singularity (unbounded first-order derivatives of the geometry coefficients) occurs. We demonstrate the relevance of the augmented system for numerical relativity. We also consider general vacuum spacetimes and solve a Riemann problem, by relying on a theorem by Rendall on the characteristic value problem for the Einstein equations.
Barnes A. P.
LeFloch Philippe G.
Schmidt Bernd G.
Stewart John M.
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