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Plane symmetric self-gravitating fluids with pressure equal to energy density

Solutions of the Cauchy problem associated with the Einstein field equations which satisfy general initial conditions are obtained under the assumptions that (1) the source of the gravitational field is a perfect fluid with pressure,p, equal to energy density,w, and (2) the space-time admits the three parameter group of motions of the Euclidean plane, that is, the space-time is plane symmetric. The results apply to the situation where the source of the gravitational field is a massless scalar field since such a source has the same stress-energy tensor as an irrotational fluid withp=w. The relation between characteristic coordinates and comoving ones is discussed and used to interpret a number of special solutions. A solution involving a shock wave is discussed.

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1. Romualdo Tabensky

   Present address: Departamento de Fisica, Universidad de Chile, Santiago, Chile

1. Physics Department, University of California, Berkeley, California, USA

   Romualdo Tabensky

2. Mathematics Department, University of California, Berkeley, California, USA

   A. H. Taub

1. Romualdo Tabensky
2. A. H. Taub

Tabensky, R., Taub, A.H. Plane symmetric self-gravitating fluids with pressure equal to energy density. Commun.Math. Phys. 29, 61–77 (1973). https://doi.org/10.1007/BF01661153

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• Received: 10 August 1972

• Issue Date: March 1973

• DOI: https://doi.org/10.1007/BF01661153

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