Black hole in closed spacetime with an anisotropic fluid

Abstract

We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of the work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static and closed space exists only when the radial pressure is negative but its size is smaller than the density. The Einstein equation is eventually casted into a first order autonomous equation on two-dimensional plane of scale-invariant variables, which are equivalent to the Tolman-Oppenheimer-Volkoff (TOV) equation in general relativity. Then, we display various solution curves numerically. An exact solution describing a black hole solution in a closed spacetime was known in Ref. [1], which solution bears a naked singularity and negative energy era. We find that the two deficits can be remedied when $\rho +3p_1>0$ and $\rho +p_1+2p_2<0$, where the second violates the strong energy condition.

15 pages, 7 figures

References in corpus (3)

• All static spherically symmetric anisotropic solutions of Einstein's equations
• Charged anisotropic matter with linear equation of state
• Vaidya-Tikekar Type Superdense Star Admitting Conformal Motion in Presence of Quintessence Field

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• Numerical Study of Instability of Fluid Black Holes
• Causal structure and the geodesics in the hairy extension of the Bertotti-Robinson spacetime