### 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 nT, the U(1) charge Q, and the nonextremality τ. 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.

Original language | English |
---|---|

Article number | 124038 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 81 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2010 Jun 18 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Black hole in the expanding universe with arbitrary power-law expansion.** / Maeda, Keiichi; Nozawa, Masato.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 81, no. 12, 124038. https://doi.org/10.1103/PhysRevD.81.124038

}

TY - JOUR

T1 - Black hole in the expanding universe with arbitrary power-law expansion

AU - Maeda, Keiichi

AU - Nozawa, Masato

PY - 2010/6/18

Y1 - 2010/6/18

N2 - 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 nT, the U(1) charge Q, and the nonextremality τ. 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.

AB - 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 nT, the U(1) charge Q, and the nonextremality τ. 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.

UR - http://www.scopus.com/inward/record.url?scp=77955339658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955339658&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.81.124038

DO - 10.1103/PhysRevD.81.124038

M3 - Article

AN - SCOPUS:77955339658

VL - 81

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 12

M1 - 124038

ER -