A P Barnes et al 2004 Class. Quantum Grav. 21 5043 doi:10.1088/0264-9381/21/22/003
A P Barnes1, P G Lefloch2, B G Schmidt3 and J M Stewart1
Show affiliationsWe 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.
04.20.Cv Fundamental problems and general formalism
04.20.Ex Initial value problem, existence and uniqueness of solutions
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 22 (21 November 2004)
Received 31 August 2004
Published 20 October 2004
A P Barnes et al 2004 Class. Quantum Grav. 21 5043
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