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

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

2010-03-15

arxiv.org/abs/1003.2849v2

Phys. Rev. D 81, 124038 (2010)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1103/PhysRevD.81.124038

We present a time-dependent and spatially inhomogeneous solution that interpolates the extremal Reissner-Nordstr\"om (RN) black hole and the Friedmann-Lema\^itre-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.

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