Exact Black Holes and Gravitational Shockwaves on Codimension-2 Branes

TL;DR

This paper derives exact gravitational solutions for black holes and shockwaves on codimension-2 branes in higher dimensions, revealing how gravity behaves at large distances and under compactification.

Contribution

It provides the first explicit example of a small black hole on a tensional 3-brane and analyzes gravitational shockwaves in higher-dimensional spacetimes.

Findings

Black hole solution threaded by a brane with a deficit angle.

Shockwaves decay as 1/r^{D-4}, showing full spacetime dimensionality.

Large-distance limit reduces to 4D Aichelburg-Sexl solution when compactified.

Abstract

We derive exact gravitational fields of a black hole and a relativistic particle stuck on a codimension-2 brane in $D$ dimensions when gravity is ruled by the bulk $D$-dimensional Einstein-Hilbert action. The black hole is locally the higher-dimensional Schwarzschild solution, which is threaded by a tensional brane yielding a deficit angle and includes the first explicit example of a `small' black hole on a tensional 3-brane. The shockwaves allow us to study the large distance limits of gravity on codimension-2 branes. In an infinite locally flat bulk, they extinguish as $1/r^{D-4}$, i.e. as $1/r^2$ on a 3-brane in $6D$, manifestly displaying the full dimensionality of spacetime. We check that when we compactify the bulk, this special case correctly reduces to the 4D Aichelburg-Sexl solution at large distances. Our examples show that gravity does not really obstruct having general matter stress-energy on codimension-2 branes, although its mathematical description may be more involved.