### Abstract

We prove that for a large class of generalized Rahdall-Sundrum type II models the characterization of the brane-gravity sector by the effective Einstein equation, Codazzi equation and the twice-contracted Gauss equation is equivalent to the bulk Einstein equation. We give the complete set of equations in the generic case of non-Z_{2}-symmetric bulk and arbitrary energy-momentum tensors both on the brane and in the bulk. Among these, the effective Einstein equation contains a varying cosmological "constant" and two new source terms. The first of these represents the deviation from Z_{2} symmetry, while the second arises from the bulk energy-momentum tensor. We apply the formalism for the case of a perfect fluid on a Friedmann brane embedded in a generic bulk. The generalized Friedmann and Raychaudhuri equations are given in a form independent of both the embedding and the bulk matter. They contain two new functions obeying a first order differential system, both depending on the bulk matter and the embedding. Then we focus oh Friedmann branes separating two nonidentical (inner or outer) regions of Reissner-Nordstrom-anti-de Sitter bulk space-times, generalizing previous non-Z_{2}-symmetric treatments. Finally the analysis is repeated for the Vaidya-anti-de Sitter bulk space-time, allowing for both ingoing and outgoing radiation in each region.

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

Article number | 124011 |

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

Volume | 68 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2003 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

**Generalized friedmann branes.** / Gergely, L.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 68, no. 12, 124011. https://doi.org/10.1103/PhysRevD.68.124011

}

TY - JOUR

T1 - Generalized friedmann branes

AU - Gergely, L.

PY - 2003

Y1 - 2003

N2 - We prove that for a large class of generalized Rahdall-Sundrum type II models the characterization of the brane-gravity sector by the effective Einstein equation, Codazzi equation and the twice-contracted Gauss equation is equivalent to the bulk Einstein equation. We give the complete set of equations in the generic case of non-Z2-symmetric bulk and arbitrary energy-momentum tensors both on the brane and in the bulk. Among these, the effective Einstein equation contains a varying cosmological "constant" and two new source terms. The first of these represents the deviation from Z2 symmetry, while the second arises from the bulk energy-momentum tensor. We apply the formalism for the case of a perfect fluid on a Friedmann brane embedded in a generic bulk. The generalized Friedmann and Raychaudhuri equations are given in a form independent of both the embedding and the bulk matter. They contain two new functions obeying a first order differential system, both depending on the bulk matter and the embedding. Then we focus oh Friedmann branes separating two nonidentical (inner or outer) regions of Reissner-Nordstrom-anti-de Sitter bulk space-times, generalizing previous non-Z2-symmetric treatments. Finally the analysis is repeated for the Vaidya-anti-de Sitter bulk space-time, allowing for both ingoing and outgoing radiation in each region.

AB - We prove that for a large class of generalized Rahdall-Sundrum type II models the characterization of the brane-gravity sector by the effective Einstein equation, Codazzi equation and the twice-contracted Gauss equation is equivalent to the bulk Einstein equation. We give the complete set of equations in the generic case of non-Z2-symmetric bulk and arbitrary energy-momentum tensors both on the brane and in the bulk. Among these, the effective Einstein equation contains a varying cosmological "constant" and two new source terms. The first of these represents the deviation from Z2 symmetry, while the second arises from the bulk energy-momentum tensor. We apply the formalism for the case of a perfect fluid on a Friedmann brane embedded in a generic bulk. The generalized Friedmann and Raychaudhuri equations are given in a form independent of both the embedding and the bulk matter. They contain two new functions obeying a first order differential system, both depending on the bulk matter and the embedding. Then we focus oh Friedmann branes separating two nonidentical (inner or outer) regions of Reissner-Nordstrom-anti-de Sitter bulk space-times, generalizing previous non-Z2-symmetric treatments. Finally the analysis is repeated for the Vaidya-anti-de Sitter bulk space-time, allowing for both ingoing and outgoing radiation in each region.

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U2 - 10.1103/PhysRevD.68.124011

DO - 10.1103/PhysRevD.68.124011

M3 - Article

VL - 68

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 12

M1 - 124011

ER -