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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
25/2007

Stability of shock waves in special and general relativity.

Heinrich Freistühler and Mohammedreza Raoofi

Abstract

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.

Received:
Mar 1, 2007
Published:
Mar 1, 2007
Keywords:
Stability, Shock Waves, Special and General Relativity

Related publications

inJournal
2007 Repository Open Access
Heinrich Freistühler and Mohammadreza Raoofi

Stability of perfect-fluid shock waves in special and general relativity

In: Classical and quantum gravity, 24 (2007) 17, pp. 4439-4455