Black Hole in the Expanding Universe with Arbitrary Power-Law Expansion

Abstract

We present a time-dependent and spatially inhomogeneous solution that interpolates the extremal Reissner-Nordström (RN) black hole and the Friedmann-Lemaître-Robertson-Walker (FLRW) universe with arbitrary power-law expansion. It is an exact solution of the $D$-dimensional Einstein-"Maxwell"-dilaton system, where two Abelian gauge fields couple to the dilaton with different coupling constants, and the dilaton field has a Liouville-type exponential potential. It is shown that the system satisfies the weak energy condition. The solution involves two harmonic functions on a $(D-1)$-dimensional Ricci-flat base space. In the case where the harmonics have a single-point source on the Euclidean space, we find that the spacetime describes a spherically symmetric charged black hole in the FLRW universe, which is characterized by three parameters: the steepness parameter of the dilaton potential $n_T$, the U$(1)$ charge $Q$, and the "nonextremality" $\tau$. In contrast with the extremal RN solution, the spacetime admits a nondegenerate Killing horizon unless these parameters are finely tuned. The global spacetime structures are discussed in detail.

22 pages, 8 figures, 1 table; v2: typos corrected, references added, version to appear in PRD

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Cited by in corpus (27)

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• Warped de Sitter compactifications
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• Cosmological brane systems in warped spacetime
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• Holography and black holes in asymptotically flat FLRW
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• Rotating black holes in an expanding universe from fake supergravity
• Dynamical angled brane
• Supersymmetry in a dynamical M-brane background
• Warped de Sitter compactifications in the scalar-tensor theory
• Spherically symmetric solutions in a FRW background
• Warped spherical compactifications in the gravity theory