Closed System of Equations on a Brane

Abstract

We obtain a generic closed system of equations on a brane that describes its inner evolution and give a method for extending solutions on the brane to the bulk. We also discuss the cosmological implications of the closed system of equations obtained. We consider bulk spaces with both spacelike and timelike extra dimension, with and without the $Z_2$ symmetry of reflection relative to the brane.

11 pages, revtex. Substantially revised version to be published in PLB

References in corpus (7)

• Large-scale cosmological perturbations on the brane
• General Brane Dynamics with R_{4} term in the Bulk
• Bulk Gravitational Field and Cosmological Perturbations on the Brane
• Einstein equations for an asymmetric brane-world
• Reflection symmetry breaking scenarios with minimal gauge form coupling in brane world cosmology
• Role of the brane curvature scalar in the brane world cosmology
• Flat Vacuum Branes Without Fine Tuning

Cited by in corpus (30)

• Braneworld models of dark energy
• Bouncing Braneworlds
• New Cosmological Singularities in Braneworld Models
• On a general class of brane-world black holes
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• Quantum effects, soft singularities and the fate of the universe in a braneworld cosmology
• Non-uniform Braneworld Stars: an Exact Solution
• New Vistas in Braneworld Cosmology
• A graceful entrance to braneworld inflation
• A Note on Asymmetric Thick Branes
• Generalised cosmological scaling solutions
• Asymmetric brane-worlds with induced gravity
• Spherically symmetric problem on the brane and galactic rotation curves
• Inverse volume corrections to emergent tachyonic inflation in loop quantum cosmology
• Spatial Ricci scalar dark energy model
• Bouncing Braneworld Cosmologies and Initial Conditions to Inflation
• Bouncing Model in Brane World Theory
• Can brane dark energy model be probed observationally by distant supernovae?
• Braneworld cosmological solutions and their stability
• Phantom-like effects in asymmetric brane embedding with induced gravity and the Gauss-Bonnet term in the Bulk
• Bounded Scalar Perturbations in Bouncing Brane World Cosmologies
• Brane world in Non-Riemannian Geometry
• Asymmetric embedding in brane cosmology
• General Bianchi IX dynamics in bouncing braneworld cosmology: homoclinic chaos and the BKL conjecture
• Gravitational Collapse and Black Hole Thermodynamics In Braneworld Scenario
• Constraints on parameters of models with extra dimension from primordial nucleosynthesis
• Cosmological constraints on parameters of one-brane models with extra dimension
• Braneworlds with timelike extra-dimension
• Traversable Lorentzian wormhole on the Shtanov-Sahni braneworld with matter obeying the energy conditions
• New asymptotic Anti-de Sitter solution with a timelike extra dimension in 5D relativity