### Abstract

We carefully investigate the gravitational equations of the brane world, in which all the matter forces except gravity are confined on the 3-brane in a 5-dimensional spacetime with Z_{2} symmetry. We derive the effective gravitational equations on the brane, which reduce to the conventional Einstein equations in the low energy limit. From our general argument we conclude that the first Randall-Sundrum-type theory predicts that the brane with a negative tension is an antigravity world and hence should be excluded from the physical point of view. Their second-type theory where the brane has a positive tension provides the correct signature of gravity. In this latter case, if the bulk spacetime is exactly anti-de Sitter spacetime, generically the matter on the brane is required to be spatially homogeneous because of the Bianchi identities. By allowing deviations from anti-de Sitter spacetime in the bulk, the situation will be relaxed and the Bianchi identities give just the relation between the Weyl tensor and the energy momentum tensor. In the present brane world scenario, the effective Einstein equations cease to be valid during an era when the cosmological constant on the brane is not well defined, such as in the case of the matter dominated by the potential energy of the scalar field.

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

Article number | 024012 |

Pages (from-to) | 1-6 |

Number of pages | 6 |

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

Volume | 62 |

Issue number | 2 |

Publication status | Published - 2000 Jul 15 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*62*(2), 1-6. [024012].

**The Einstein equations on the 3-brane world.** / Shiromizu, Tetsuya; Maeda, Keiichi; Sasaki, Misao.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 62, no. 2, 024012, pp. 1-6.

}

TY - JOUR

T1 - The Einstein equations on the 3-brane world

AU - Shiromizu, Tetsuya

AU - Maeda, Keiichi

AU - Sasaki, Misao

PY - 2000/7/15

Y1 - 2000/7/15

N2 - We carefully investigate the gravitational equations of the brane world, in which all the matter forces except gravity are confined on the 3-brane in a 5-dimensional spacetime with Z2 symmetry. We derive the effective gravitational equations on the brane, which reduce to the conventional Einstein equations in the low energy limit. From our general argument we conclude that the first Randall-Sundrum-type theory predicts that the brane with a negative tension is an antigravity world and hence should be excluded from the physical point of view. Their second-type theory where the brane has a positive tension provides the correct signature of gravity. In this latter case, if the bulk spacetime is exactly anti-de Sitter spacetime, generically the matter on the brane is required to be spatially homogeneous because of the Bianchi identities. By allowing deviations from anti-de Sitter spacetime in the bulk, the situation will be relaxed and the Bianchi identities give just the relation between the Weyl tensor and the energy momentum tensor. In the present brane world scenario, the effective Einstein equations cease to be valid during an era when the cosmological constant on the brane is not well defined, such as in the case of the matter dominated by the potential energy of the scalar field.

AB - We carefully investigate the gravitational equations of the brane world, in which all the matter forces except gravity are confined on the 3-brane in a 5-dimensional spacetime with Z2 symmetry. We derive the effective gravitational equations on the brane, which reduce to the conventional Einstein equations in the low energy limit. From our general argument we conclude that the first Randall-Sundrum-type theory predicts that the brane with a negative tension is an antigravity world and hence should be excluded from the physical point of view. Their second-type theory where the brane has a positive tension provides the correct signature of gravity. In this latter case, if the bulk spacetime is exactly anti-de Sitter spacetime, generically the matter on the brane is required to be spatially homogeneous because of the Bianchi identities. By allowing deviations from anti-de Sitter spacetime in the bulk, the situation will be relaxed and the Bianchi identities give just the relation between the Weyl tensor and the energy momentum tensor. In the present brane world scenario, the effective Einstein equations cease to be valid during an era when the cosmological constant on the brane is not well defined, such as in the case of the matter dominated by the potential energy of the scalar field.

UR - http://www.scopus.com/inward/record.url?scp=18144383194&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18144383194&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:18144383194

VL - 62

SP - 1

EP - 6

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 2

M1 - 024012

ER -