Static relativistic perfect fluids with spherical, plane, or hyperbolic symmetry

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Abstract
This article examines the Einstein field of equations of general relativity, when the source of the gravitational field is a perfect fluid, and the geometry is static and possesses spherical, plane, or hyperbolic symmetry. This examination unifies, extends, and amends some earlier works. It is shown that a previous qualitative treatment of static spherically symmetric perfect fluids that obey a γ‐law equation of state can be extended to include the cases of plane and hyperbolic symmetry. In the case of plane symmetry, the exact solution is provided for general values of γ. This indicates defects in an earlier prescription that was given for a general equation of state.

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