### Abstract

Time evolution of a black hole lattice universe with a positive cosmological constant Λ is simulated. The vacuum Einstein equations are numerically solved in a cubic box with a black hole in the center. Periodic boundary conditions on all pairs of opposite faces are imposed. Configurations of marginally trapped surfaces are analyzed. We describe the time evolution of not only black hole horizons, but also cosmological horizons. Defining the effective scale factor by using the area of a surface of the cubic box, we compare it with that in the spatially flat dust dominated Friedmann- Lemaître-Robertson-Walker (FLRW) universe with the same value of Λ. It is found that the behavior of the effective scale factor is well approximated by that in the FLRW universe. Our result suggests that local inhomogeneities do not significantly affect the global expansion law of the Universe irrespective of the value of Λ.

Original language | English |
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Article number | 123502 |

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

Volume | 89 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2014 Jun 3 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Black hole universe with a cosmological constant.** / Yoo, Chul Moon; Okawa, Hirotada.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 89, no. 12, 123502. https://doi.org/10.1103/PhysRevD.89.123502

}

TY - JOUR

T1 - Black hole universe with a cosmological constant

AU - Yoo, Chul Moon

AU - Okawa, Hirotada

PY - 2014/6/3

Y1 - 2014/6/3

N2 - Time evolution of a black hole lattice universe with a positive cosmological constant Λ is simulated. The vacuum Einstein equations are numerically solved in a cubic box with a black hole in the center. Periodic boundary conditions on all pairs of opposite faces are imposed. Configurations of marginally trapped surfaces are analyzed. We describe the time evolution of not only black hole horizons, but also cosmological horizons. Defining the effective scale factor by using the area of a surface of the cubic box, we compare it with that in the spatially flat dust dominated Friedmann- Lemaître-Robertson-Walker (FLRW) universe with the same value of Λ. It is found that the behavior of the effective scale factor is well approximated by that in the FLRW universe. Our result suggests that local inhomogeneities do not significantly affect the global expansion law of the Universe irrespective of the value of Λ.

AB - Time evolution of a black hole lattice universe with a positive cosmological constant Λ is simulated. The vacuum Einstein equations are numerically solved in a cubic box with a black hole in the center. Periodic boundary conditions on all pairs of opposite faces are imposed. Configurations of marginally trapped surfaces are analyzed. We describe the time evolution of not only black hole horizons, but also cosmological horizons. Defining the effective scale factor by using the area of a surface of the cubic box, we compare it with that in the spatially flat dust dominated Friedmann- Lemaître-Robertson-Walker (FLRW) universe with the same value of Λ. It is found that the behavior of the effective scale factor is well approximated by that in the FLRW universe. Our result suggests that local inhomogeneities do not significantly affect the global expansion law of the Universe irrespective of the value of Λ.

UR - http://www.scopus.com/inward/record.url?scp=84902957050&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevD.89.123502

DO - 10.1103/PhysRevD.89.123502

M3 - Article

VL - 89

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 12

M1 - 123502

ER -