Class of perfect fluid metrics with flat three-dimensional hypersurfaces

Journal Article · Mon Sep 01 00:00:00 EDT 1986 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.527005· OSTI ID:5317348

Wolf, T

The class of perfect fluid and vacuum space-times with a family of flat three-slices and a tensor of exterior curvature covariantly constant within these slices is examined and the corresponding solutions are found. It is shown that this class contains the class of metrics with three commuting Killing vectors. Therefore, e.g., all known stationary metrics with cylindrical or plane symmetry are generalized. An instruction is given for constructing perfect fluid metrics with this symmetry and a connection to a vacuum across surfaces p-italic = 0. Thereby the equation of state of the interior rotating perfect fluid can be arbitrarily chosen and the positivity of density and pressure can be forced. A geometric criterion of the interior metric with rotating matter is found that decides whether the exterior solution is stationary or static. Besides solutions with three symmetries, inhomogeneous metrics also are found. Among them is a solution with one symmetry and rotating, expanding, shearing, and accelerating perfect fluid. All resulting vacuum solutions are already known.

• Research Organization: Sektion Physik, Friedrich Schiller Universitaet Jena, GDR 6900 Jena, Max-Wien-Platz 1, German Democratic Republic
• OSTI ID: 5317348
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 27:9; ISSN JMAPA
• Country of Publication: United States
• Language: English

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GENERAL RELATIVITY THEORY
IDEAL FLOW
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MOTION
PHYSICAL PROPERTIES
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