Brane Dynamics, the Polytropic Gas and Conformal Bulk Fields

TL;DR

This paper explores exact 5D solutions in the Randall-Sundrum model with bulk matter, analyzing how polytropic matter on the brane influences its dynamics and the conditions for regularity or singularity.

Contribution

It provides new exact solutions for brane-world scenarios with bulk matter, linking conformal bulk fields to brane polytropic dynamics and their regularity conditions.

Findings

Gravity is localized near the brane in these solutions.

Polytropic matter dynamics can be singular or regular depending on conditions.

Conformal bulk fields are associated with the brane's polytropic behavior.

Abstract

We consider in the Randall-Sundrum scenario the dynamics of a spherically symmetric 3-brane world when matter fields exist in the bulk. We determine exact 5-dimensional solutions which localize gravity near the brane and describe the dynamics of homogeneous polytropic matter on the brane. We show that these geometries are associated with a well defined conformal class of bulk matter fields. We analyze the effective polytropic dynamics on the brane identifying conditions which define it as singular or as globally regular.