Schwarzschild Solution on the Brane

TL;DR

This paper demonstrates that the Schwarzschild solution can exist on a brane within brane world models, under specific conditions involving brane matter and bulk effects, including a conformally flat bulk and fine-tuned vacuum energy.

Contribution

It shows the conditions under which Schwarzschild solutions are possible in brane world scenarios, extending understanding of black hole solutions in higher-dimensional models.

Findings

Schwarzschild solution is possible with specific brane matter configurations.

Conformally flat bulk space supports Schwarzschild solutions.

Fine-tuned vacuum energy enables Schwarzschild vacuum solutions.

Abstract

In this communication we have shown that Schwarzschild solution is possible in brane world for some specific choices of brane matter and the non local effects from the bulk. A conformally flat bulk space time with fine-tuned vacuum energy (brane tension) shows that, Schwarzschild solution may also be the vacuum solution for brane world scenario.