Brane-world stars from minimal geometric deformation, and black holes

TL;DR

This paper develops analytical models of spherically symmetric stars in the brane-world, linking interior solutions to external metrics with ADM mass and tidal charge, and explores black hole limits with implications for minimum black hole mass.

Contribution

It introduces the minimal geometric deformation method to derive interior solutions in brane-world stars and black holes, connecting them to external tidal charge and ADM mass.

Findings

Derived a relation between star radius, mass, and tidal charge.

Obtained black hole metrics with tidal charge determined by mass and brane tension.

Discussed minimum mass for semiclassical black holes.

Abstract

We build analytical models of spherically symmetric stars in the brane-world, in which the external space-time contains both an ADM mass and a tidal charge. In order to determine the interior geometry, we apply the principle of minimal geometric deformation, which allows one to map General Relativistic solutions to solutions of the effective four-dimensional brane-world equations. We further restrict our analysis to stars with a radius linearly related to the total General Relativistic mass, and obtain a general relation between the latter, the brane-world ADM mass and the tidal charge. In these models, the value of the star's radius can then be taken to zero smoothly, thus obtaining brane-world black hole metrics with a tidal charge solely determined by the mass of the source and the brane tension. General conclusions regarding the minimum mass for semiclassical black holes will also be drawn.