The canonical approach to the thermodynamics of black holes attached to cosmic strings is extended to include Hawking radiation. This radiation is modeled by the expctation values of the renormalized thermal equilibrium stress-energy tensors of free conformally invariant quantum fields propagating in the Schwarzschild black-hole background. The quantum nature of gravity is described by the path-integral approach to quantum gravity rather than by a similar tensor for gravitons. The back reaction and resulting new equilibrium metric are calculated perturbatively. This metric is used to define a class of metrics. Every member of this class represents the real Euclidean section of a static spacetime which describes a black hole attached to a cosmic string in thermal equilibrium with the Hawking radiation. We then examine the thermodynamical stability of microcanonical systems by using the canonical formalism.

• Received 23 October 1992

DOI:https://doi.org/10.1103/PhysRevD.47.2260