Using the Euclidean action with constraints eliminated, we study the thermodynamics of the simplest spacetime that models a cosmic string threading a black hole. A comparison with ordinary black holes under equivalent boundary conditions, either canonical or microcanonical, shows that the merging of a black hole and a string is not thermodynamically forbidden. If such a system exists, then according to the model studied here it will not spontaneously decay to a black hole without a cosmic string.

• Received 25 June 1990

DOI:https://doi.org/10.1103/PhysRevD.42.3580