Constant Curvature Black Hole and Dual Field Theory

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 ${\cal M}_4\times S^1$, its exterior is not static 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 one of the dual conformal field theory. It is found that the trace of the tensor does indeed vanish, as expected. Through the surface counterterm approach, computing the Euclidean action of the black hole, we obtain the mass and entropy associated with the black hole, and find both of them are negative. We also compare our results with related discussions by other authors, in particular with the study of "bubbles of nothing" in AdS spaces.