Constant Curvature Black Hole and Dual Field Theory

TL;DR

This work analyzes a five-dimensional constant-curvature black hole in AdS$_5$, obtained by identifying points along a Killing vector, which yields a time-dependent exterior and a boundary with geometry $dS_3\times S^1$. Using holographic renormalization with a surface counterterm, the authors compute the quasilocal gravitational stress-energy and map it to the dual CFT stress-energy on the boundary, finding a traceless stress tensor with negative energy density and no Casimir contribution, independent of the mass parameter $r_+$. The boundary CFT resides on a dynamical spacetime, and the results tie the spacetime to the concept of a bubble of nothing in the $r_0=0$ limit discussed by Balasubramanian and Ross. The study clarifies holographic aspects of time-dependent backgrounds and their relation to bubbles of nothing, and it outlines directions for further work such as Wilson loops and higher-dimensional generalizations.

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.