Hamiltonian theory of brane-world gravity

TL;DR

This paper develops a Hamiltonian framework for brane-world gravity using a 3+1+1 decomposition, enabling advanced analysis of cosmological and black hole phenomena in higher-dimensional models.

Contribution

It introduces a canonical theory of brane cosmology based on a novel 3+1+1 decomposition, facilitating new approaches to problems in brane-world gravity.

Findings

Provides Hamiltonian equations for brane-world scenarios

Enables study of initial value problems and stability

Supports analysis of black holes and quantum aspects

Abstract

A brane-world universe consists of a 4-dimensional brane embedded into a 5-dimensional space-time (bulk). We apply the Arnowitt-Deser-Misner decomposition to the brane-world, which results in a 3+1+1 break-up of the bulk. We present the canonical theory of brane cosmology based on this decomposition. The Hamiltonian equations allow for the study of any physical phenomena in brane gravity. This method gives new prospects for studying the initial value problem, stability analysis, brane black holes, cosmological perturbation theory and canonical quantization in brane-worlds.