On Gauge Choice of Spherically Symmetric 3-Branes

TL;DR

This paper investigates how gauge choices influence the matter field dependencies in spherically symmetric 3-branes embedded in higher-dimensional spaces, revealing restrictions imposed by junction conditions.

Contribution

It demonstrates that Israel's junction conditions severely limit matter field dependencies on spacetime coordinates under specific gauge choices.

Findings

Scalar and Yang-Mills fields are restricted to time or radial dependence.

Perfect fluid must be co-moving with the brane.

Gauge choice constrains matter field behavior.

Abstract

Gauge choice for a spherically symmetric 3-brane embedded in a D-dimensional bulk with arbitrary matter fields on and off the brane is studied. It is shown that Israel's junction conditions across the brane restrict severely the dependence of the matter fields on the spacetime coordinates. As examples, a scalar field or a Yang-Mills potential can be only either time-dependent or radial-coordinate dependent for the chosen gauge, while for a perfect fluid it must be co-moving.