Dark Radiation Dynamics on the Brane

TL;DR

This paper explores the behavior of dark radiation in a brane-world scenario, deriving exact solutions and analyzing conditions for regularity, singularity, and gravity confinement, including potential phase transitions during collapse.

Contribution

It provides new exact dynamical solutions for dark radiation on a brane and analyzes conditions for their regularity and the confinement of gravity.

Findings

Exact inhomogeneous solutions depend on brane parameters.

Conditions for singular or regular solutions are identified.

Gravity confinement may break down during collapse.

Abstract

We investigate the dynamics of a spherically symmetric vaccum on a Randall and Sundrum 3-brane world. Under certain natural conditions, the effective Einstein equations on the brane form a closed system for spherically symmetric dark radiation. We determine exact dynamical and inhomogeneous solutions, which are shown to depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial energy configuration. We identify the conditions defining these solutions as singular or as globally regular. Finally, we discuss the confinement of gravity to the vicinity of the brane and show that a phase transition to a regime where gravity is not bound to the brane may occur at short distances during the collapse of positive dark energy density on a realistic de Sitter brane.