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

Freistühler, Heinrich; Raoofi, Mohammedreza

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

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Date

2007

Authors

Freistühler, Heinrich

Raoofi, Mohammedreza

DOI (citable link)

10.1088/0264-9381/24/17/011

Collections

Mathematik und Statistik

Publication type

Journal article

Publication status

Published

Published in

Classical and Quantum Gravity ; 24 (2007), 17. - pp. 4439-4455. - ISSN 0264-9381. - eISSN 1361-6382

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–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.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

FREISTÜHLER, Heinrich, Mohammedreza RAOOFI, 2007. Stability of perfect-fluid shock waves in special and general relativity. In: Classical and Quantum Gravity. 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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