ar X iv : g r - qc / 0 21 10 35 v 1 1 1 N ov 2 00 2 A note on Schwarzschild black hole thermodynamics in a magnetic universe Eugen

We prove that the thermodynamic properties of a Schwarzschild black hole are unaffected by an external magnetic field passing through it. Apart from the background substraction prescription, this result is obtained also by using a counterterm method. The black holes created in astrophysical processes are expected to be well described by asymptotically flat solutions of Einstein equations. However, there is also a great interest in black holes with other kind of asymptotic infinities. It particular, it is of interest to determine the effects that occur when black holes are placed in an external background field, extending to infinity. Most of the work on this subject, including pair creation of charged black holes has been done in a Einstein-Maxwell theory and in a generalization of this theory which include a dilaton Φ, whose action is