Abstract
A shock wave in a self-gravitating fluid obeying the equation of state: pressure equal to energy density is shown to travel with the velocity of light in a space-time determined by the Einstein field equations. The jump conditions that must be satisfied by the hydrodynamic variables are derived and discussed as are those that must be satisfied by the metric tensor and its derivatives. The latter conditions are obtained by using a variational principle.
Similar content being viewed by others
References
Tabensky, R., Taub, A. H.: Commun. math. Phys.29, 61–77 (1973).
Taub, A. H.: Variational principles in general relativity, Chapter III in Relativistic Fluid Dynamics; Centro Internazionale Mathematico Estivo, Bressanone 7–16 July 1970, Edizioni Cremonese, Roma 1971.
Lichnerowicz, A.: Relativistic hydrodynamics and magnetohydrodynamics; New York: W. A. Benjamin, Inc. 1967.
Papapetrou, A., Treder, H.: Math. Nachr.23, 371–384 (1961).
Lichnerowicz, A.: Compt. Rend.273, 528–532 (1971).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Taub, A.H. General relativistic shock waves in fluids for which pressure equals energy density. Commun.Math. Phys. 29, 79–88 (1973). https://doi.org/10.1007/BF01661154
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01661154