Constant Curvature Black Hole and Dual Field Theory

TL;DR

This paper studies a five-dimensional constant curvature black hole with a dynamic boundary spacetime, analyzing its gravitational and dual field theory properties, including stress-energy tensors and its relation to the bubble of nothing.

Contribution

It introduces a novel five-dimensional black hole with a dynamic boundary and computes its dual stress-energy tensor, linking it to the bubble of nothing scenario.

Findings

The dual stress-energy tensor is traceless.

The black hole spacetime corresponds to the bubble of nothing.

The boundary metric is a three-dimensional de Sitter space times a circle.

Abstract

We consider a five-dimensional constant curvature black hole, which is constructed by identifying some points along a Killing vector in a five-dimensional AdS space. The black hole has the topology M_4 times S^1, its exterior is time-dependent and its boundary metric is of the form of a three-dimensional de Sitter space times a circle, which means that the dual conformal field theory resides on a dynamical spacetime. We calculate the quasilocal stress-energy tensor of the gravitational background and then the stress-energy tenor of the dual conformal field theory. It is found that the trace of the tensor does indeed vanish, as expected. Further we find that the constant curvature black hole spacetime is just the "bubble of nothing" resulting from Schwarzschild-AdS black holes when the mass parameter of the latter vanishes.