Brane World Dynamics and Conformal Bulk Fields

TL;DR

This paper explores the dynamics of a spherically symmetric brane world with bulk matter, deriving exact solutions that demonstrate gravity localization and consistency with 4D observations in a Randall-Sundrum framework.

Contribution

It introduces new exact dynamical collapse solutions in brane world models with conformal bulk fields, expanding understanding of gravity localization and brane-bulk interactions.

Findings

Derived exact solutions for brane dynamics with conformal bulk matter.

Showed gravity can localize near the brane in these models.

Confirmed consistency with 4D effective theory for brane observers.

Abstract

In the Randall-Sundrum scenario we investigate the dynamics of a spherically symmetric 3-brane world when matter fields are present in the bulk. To analyze the 5-dimensional Einstein equations we employ a global conformal transformation whose factor characterizes the $Z_2$ symmetric warp. We find a new set of exact dynamical collapse solutions which localize gravity in the vicinity of the brane for a stress-energy tensor of conformal weight -4 and a warp factor that depends only on the coordinate of the fifth dimension. Geometries which describe the dynamics of inhomogeneous dust and generalized dark radiation on the brane are shown to belong to this set. The conditions for singular or globally regular behavior and the static marginally bound limits are discussed for these examples. Also explicitly demonstrated is complete consistency with the effective point of view of a 4-dimensional observer who is confined to the brane and makes the same assumptions about the bulk degrees of freedom.