Analytic solution for a static black hole in RSII model

TL;DR

This paper derives an analytic static black hole solution in the RSII brane-world model, showing it encodes quantum effects and differs from Schwarzschild, with implications for understanding black holes in higher-dimensional theories.

Contribution

The paper provides the first analytic static black hole solutions in RSII with non-empty bulk, challenging previous assumptions about their non-existence.

Findings

The solution encodes quantum gravitational effects.

The bulk matter is non-singular and physically reasonable.

The solution cannot be transformed into Schwarzschild form.

Abstract

We present here a static solution for a large black hole (whose horizon radius is larger than the AdS radius) located on the brane in RSII model. According to some arguments based on the AdS/CFT conjecture, a solution for the black hole located on the brane in RSII model must encode quantum gravitational effects and therefore can not be static. We demonstrated that a static solution can be found if the bulk is not empty. The stress energy tensor of the matter distribution in the bulk for the solution we found is physical (i.e. it is non-singular with the energy density and pressure not violating any energy conditions). However, the solution can not be transformed into the Schwarzschild-like form and does not reduce to the Schwarzschild solution on the brane. We also present two other related static solutions. At the end, we discuss why the numerical methods failed so far in finding static solutions in this context, including the solutions we found analytically here.