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The Einstein Equations on the 3-Brane World

10 Pith papers cite this work. Polarity classification is still indexing.

10 Pith papers citing it
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 $Z_2$ 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 (RS1) [hep-ph/9905221] predicts that the brane with the negative tension is an anti-gravity world and hence should be excluded from the physical point of view. Their second-type theory (RS2) [hep-th/9906064] where the brane has the positive tension provides the correct signature of gravity. In this latter case, if the bulk spacetime is exactly anti-de Sitter, generically the matter on the brane is required to be spatially homogeneous because of the Bianchi identities. By allowing deviations from anti-de Sitter 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.

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background 3 method 1

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years

2026 8 2025 2

representative citing papers

Cosmic Inflation From Regular Black Holes

gr-qc · 2026-04-06 · unverdicted · novelty 7.0

Regular black holes in the bulk of quasi-topological gravity drive a de Sitter inflationary phase on the brane at small scales, with e-fold number set by the ratio of black hole radius to higher-curvature scale.

Massive Graviton Dark Matter from a Gapped Continuum

hep-th · 2026-07-08 · conditional · novelty 6.0

Radiative corrections pull an isolated, long-lived massive graviton out of the gapped linear-dilaton continuum, giving a sub-MeV dark-matter candidate that can coexist with a holographic fluid component.

Quasinormal modes of the thick braneworld in $f(T)$ gravity

gr-qc · 2026-04-09 · unverdicted · novelty 5.0

In a thick braneworld model with f(T) = T + α T², the parameter α induces brane splitting and alters the decay rates of quasinormal modes, with two numerical methods agreeing on the low-overtone spectrum.

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