  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.
