### Abstract

We carefully investigate the gravitational perturbation of the Randall-Sundrum (RS) single brane-world solution [L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999)], based on a covariant curvature tensor formalism recently developed by us. Using this curvature formalism, it is known that the "electric" part of the five-dimensional Weyl tensor, denoted by E_{μν}, gives the leading order correction to the conventional Einstein equations on the brane. We consider the general solution of the perturbation equations for the five-dimensional Weyl tensor caused by the matter fluctuations on the brane. By analyzing its asymptotic behavior in the direction of the fifth dimension, we find the curvature invariant diverges as we approach the Cauchy horizon. However, in the limit of asymptotic future in the vicinity of the Cauchy horizon, the curvature invariant falls off fast enough to render the divergence harmless to the brane world. We also obtain the asymptotic behavior of E_{μν} on the brane at spatial infinity, assuming that the matter perturbation is localized. We find it falls off sufficiently fast and will not affect the conserved quantities at spatial infinity. This indicates strongly that the usual conservation law, such as the ADM energy conservation, holds on the brane as far as asymptotically flat spacetimes are concerned.

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

Article number | 024008 |

Pages (from-to) | 1-8 |

Number of pages | 8 |

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), 1-8. [024008].

**Gravity, stability, and energy conservation on the Randall-Sundrum brane world.** / Sasaki, Misao; Shiromizu, Tetsuya; Maeda, Keiichi.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 62, no. 2, 024008, pp. 1-8.

}

TY - JOUR

T1 - Gravity, stability, and energy conservation on the Randall-Sundrum brane world

AU - Sasaki, Misao

AU - Shiromizu, Tetsuya

AU - Maeda, Keiichi

PY - 2000/7/15

Y1 - 2000/7/15

N2 - We carefully investigate the gravitational perturbation of the Randall-Sundrum (RS) single brane-world solution [L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999)], based on a covariant curvature tensor formalism recently developed by us. Using this curvature formalism, it is known that the "electric" part of the five-dimensional Weyl tensor, denoted by Eμν, gives the leading order correction to the conventional Einstein equations on the brane. We consider the general solution of the perturbation equations for the five-dimensional Weyl tensor caused by the matter fluctuations on the brane. By analyzing its asymptotic behavior in the direction of the fifth dimension, we find the curvature invariant diverges as we approach the Cauchy horizon. However, in the limit of asymptotic future in the vicinity of the Cauchy horizon, the curvature invariant falls off fast enough to render the divergence harmless to the brane world. We also obtain the asymptotic behavior of Eμν on the brane at spatial infinity, assuming that the matter perturbation is localized. We find it falls off sufficiently fast and will not affect the conserved quantities at spatial infinity. This indicates strongly that the usual conservation law, such as the ADM energy conservation, holds on the brane as far as asymptotically flat spacetimes are concerned.

AB - We carefully investigate the gravitational perturbation of the Randall-Sundrum (RS) single brane-world solution [L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999)], based on a covariant curvature tensor formalism recently developed by us. Using this curvature formalism, it is known that the "electric" part of the five-dimensional Weyl tensor, denoted by Eμν, gives the leading order correction to the conventional Einstein equations on the brane. We consider the general solution of the perturbation equations for the five-dimensional Weyl tensor caused by the matter fluctuations on the brane. By analyzing its asymptotic behavior in the direction of the fifth dimension, we find the curvature invariant diverges as we approach the Cauchy horizon. However, in the limit of asymptotic future in the vicinity of the Cauchy horizon, the curvature invariant falls off fast enough to render the divergence harmless to the brane world. We also obtain the asymptotic behavior of Eμν on the brane at spatial infinity, assuming that the matter perturbation is localized. We find it falls off sufficiently fast and will not affect the conserved quantities at spatial infinity. This indicates strongly that the usual conservation law, such as the ADM energy conservation, holds on the brane as far as asymptotically flat spacetimes are concerned.

UR - http://www.scopus.com/inward/record.url?scp=18144373479&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18144373479&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:18144373479

VL - 62

SP - 1

EP - 8

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 2

M1 - 024008

ER -