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arXiv · hep-th/0309152

Covariant Gravitational Equations on Brane World with Gauss-Bonnet term

Kei-ichi Maeda·Takashi Torii
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Abstract

We present the covariant gravitational equations to describe a four-dimensional brane world in the case with the Gauss-Bonnet term in a bulk spacetime, assuming that gravity is confined on the $Z_2$ symmetric brane. It contains some components of five-dimensional Weyl curvature ($E_{μν}$) which describes all effects from the bulk spacetime just as in the case of the Randall-Sundrum second model. Applying this formalism to cosmology, we derive the generalized Friedmann equation and calculate the Weyl curvature term, which is directly obtained from a black hole solution.

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Kei-ichi Maeda, Takashi Torii. 2003-09-16. Covariant Gravitational Equations on Brane World with Gauss-Bonnet term. https://doi.org/10.1103/physrevd.69.024002

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