Dark Radiation and Localization of Gravity on the Brane

TL;DR

This paper explores the behavior of dark radiation in the Randall-Sundrum brane world, deriving exact solutions and analyzing gravity localization, revealing potential phase transitions during collapse scenarios.

Contribution

It provides new exact solutions for dark radiation dynamics on the brane and investigates conditions for gravity localization and phase transitions.

Findings

Exact inhomogeneous solutions depend on brane parameters

Conditions for singular or regular solutions identified

Gravity may propagate away from the brane during collapse

Abstract

We discuss the dynamics of a spherically symmetric dark radiation vaccum in the Randall-Sundrum brane world scenario. Under certain natural assumptions we show that the Einstein equations on the brane form a closed system. For a de Sitter brane we determine exact dynamical and inhomogeneous solutions which depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial configuration. We define the conditions leading to singular or globally regular solutions. We also analyse the localization of gravity near the brane and show that a phase transition to a regime where gravity propagates away from the brane may occur at short distances during the collapse of positive dark energy density.