On-brane data for braneworld stars

TL;DR

This paper derives the complete on-brane equations for static spherically symmetric stars in a Randall--Sundrum braneworld, providing a foundation for understanding their 5D bulk geometry and extending to solid objects.

Contribution

It provides the first complete solution to the on-brane Gauss and Codazzi equations for braneworld stars, enabling analysis of their bulk spacetime.

Findings

Derived on-brane boundary data for braneworld stars

Outlined propagation of boundary data into the bulk

Generalized method to solid objects like planets

Abstract

Stellar structure in braneworlds is markedly different from that in ordinary general relativity. As an indispensable first step towards a more general analysis, we completely solve the ``on brane'' 4-dimensional Gauss and Codazzi equations for an arbitrary static spherically symmetric star in a Randall--Sundrum type II braneworld. We then indicate how this on-brane boundary data should be propagated into the bulk in order to determine the full 5-dimensional spacetime geometry. Finally, we demonstrate how this procedure can be generalized to solid objects such as planets.