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

Misao Sasaki, Tetsuya Shiromizu, Keiichi Maeda

    Research output: Contribution to journalArticle

    263 Citations (Scopus)

    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 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.

    Original languageEnglish
    Article number024008
    Pages (from-to)1-8
    Number of pages8
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume62
    Issue number2
    Publication statusPublished - 2000 Jul 15

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    Brane World
    Energy Conservation
    energy conservation
    Branes
    conservation
    Gravity
    curvature
    gravitation
    Weyl Tensor
    Curvature
    tensors
    Perturbation
    perturbation
    infinity
    Cauchy
    horizon
    Horizon
    Covariant tensor
    Asymptotic Behavior
    Infinity

    ASJC Scopus subject areas

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

    Cite this

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

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 62, No. 2, 024008, 15.07.2000, p. 1-8.

    Research output: Contribution to journalArticle

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