Bulk shape of brane-world black holes

TL;DR

This paper introduces a method using multipole expansion to analyze the bulk shape of static spherically symmetric brane-world black holes, revealing that their horizons are likely flat pancakes for astrophysical sources.

Contribution

It presents a novel approach combining multipole expansion with the parameterized post-Newtonian formalism to study brane-world black hole geometries.

Findings

Horizon shape is likely a flat pancake for astrophysical sources.

The method allows exact integration of equations along the extra dimension.

Application to existing solutions confirms the horizon shape.

Abstract

We propose a method to extend into the bulk asymptotically flat static spherically symmetric brane-world metrics. We employ the multipole (1/r) expansion in order to allow exact integration of the relevant equations along the (fifth) extra coordinate and make contact with the parameterized post-Newtonian formalism. We apply our method to three families of solutions previously appeared as candidates of black holes in the brane world and show that the shape of the horizon is very likely a flat ``pancake'' for astrophysical sources.