The Einstein equations on the 3-brane world

Tetsuya Shiromizu, Keiichi Maeda, Misao Sasaki

    Research output: Contribution to journalArticle

    1219 Citations (Scopus)

    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 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.

    Original languageEnglish
    Article number024012
    Pages (from-to)1-6
    Number of pages6
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume62
    Issue number2
    Publication statusPublished - 2000 Jul 15

    Fingerprint

    Brane World
    Einstein Equations
    Einstein equations
    Branes
    antigravity
    Space-time
    tensors
    gravitation
    Type Theory
    Gravity
    kinetic energy
    potential energy
    signatures
    scalars
    Weyl Tensor
    deviation
    Energy-momentum Tensor
    symmetry
    Cosmological Constant
    Energy

    ASJC Scopus subject areas

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

    Cite this

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

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 62, No. 2, 024012, 15.07.2000, p. 1-6.

    Research output: Contribution to journalArticle

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