3D black holes on a 2-brane in 4D Minkowski space

TL;DR

This paper explores three-dimensional black hole solutions on a 2-brane embedded in four-dimensional Minkowski space, revealing how local BTZ and SdS_3 solutions can transition to four-dimensional Schwarzschild-like black holes without a cosmological constant.

Contribution

It demonstrates the existence of vacuum black hole solutions in 2+1 dimensions on a 2-brane in 4D space without cosmological constants and shows the flow from lower to higher dimensional black hole solutions.

Findings

Vacuum black hole solutions exist in 2+1 dimensions without cosmological constants.

Local BTZ and SdS_3 solutions can evolve into 4D Schwarzschild-like black holes.

A crossover scale determines the transition between 3D and 4D gravitational effects.

Abstract

We investigate three-dimensional black hole solutions in the realm of pure and new massive gravity in 2+1 dimensions induced on a 2-brane embedded in a flat four-dimensional spacetime. There is no cosmological constant neither on the brane nor on the four-dimensional bulk. Only gravitational fields are turned on and we indeed find vacuum solutions as black holes in 2+1 dimensions even in the absence of any cosmological solution. There is a crossover scale that controls how far the three- or four-dimensional gravity manifests on the 2-brane. Our solutions also indicate that local BTZ and SdS_3 solutions can flow to local four-dimensional Schwarzschild like black holes, as one probes from small to large distances, which is clearly a higher dimensional manifestation on the 2-brane. This is similar to the DGP scenario where the effects of extra dimensions for large probed distances along the brane manifest.