Stability of shock waves in special and general relativity.
Heinrich Freistühler and Mohammedreza Raoofi
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Submission date: 01. Mar. 2007
published in: Classical and quantum gravity, 24 (2007) 17, p. 4439-4455
DOI number (of the published article): 10.1088/0264-9381/24/17/011
with the following different title: Stability of perfect-fluid shock waves in special and general relativity
Keywords and phrases: Stability, Shock Waves,, Special and General Relativity
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For general relativity, the persistence problem of shock fronts in perfect fluids is also a continuation problem for a pseudo-Riemannian metric of reduced regularity. In this paper, the problem is solved by considerations on a Cauchy problem which combines a well-known formulation of the Einstein- Euler equations as a first-order symmetric hyperbolic system and Rankine- Hugoniot type jump conditions for the fluid variables with an extra (non-)jump condition for the first derivatives of the metric. This ansatz corresponds to the use of space-time coordinates which are natural in the sense of Israel and harmonic at the same time. As in non-relativistic settings, the shock front must satisfy a Kreiss-Lopatinski condition in order for the persistence result to apply. The paper also shows that under standard assumptions on the fluid’s equation of state, this condition actually holds for all meaningful shock data.