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

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2007
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Raoofi, Mohammedreza
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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–Hugoniottype 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.

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510 Mathematik
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ISO 690FREISTÜHLER, Heinrich, Mohammedreza RAOOFI, 2007. Stability of perfect-fluid shock waves in special and general relativity. In: Classical and Quantum Gravity. 2007, 24(17), pp. 4439-4455. ISSN 0264-9381. eISSN 1361-6382. Available under: doi: 10.1088/0264-9381/24/17/011
BibTex
@article{Freistuhler2007-09-07Stabi-40756,
  year={2007},
  doi={10.1088/0264-9381/24/17/011},
  title={Stability of perfect-fluid shock waves in special and general relativity},
  number={17},
  volume={24},
  issn={0264-9381},
  journal={Classical and Quantum Gravity},
  pages={4439--4455},
  author={Freistühler, Heinrich and Raoofi, Mohammedreza}
}
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