Entropy of massive fields near a black hole and vacuum polarization: thermodynamics without statistical mechanics

Starting from the Frolov-Zel'nikov stress-energy tenser of quantum massive fields in the Schwarzschild background, we recover the contribution S-q of these field into the entropy of a black hole. For fermions with the spin s = 1/2 S-q > 0, for scalar fields S-q > 0 provided the coupling parameter is restricted to some interval, and S-q < 0 for vector fields. The appearance of negative values of S-q is attributed to the fact that in the situation under discussion there are no real quanta to contribute to the entropy, so S-q is due to vacuum polarization entirely and has nothing to do with the statistical-mechanical entropy. We also consider the spacetime with. an acceleration horizon - the Bertotti-Robison spacetime - and show that S-q = 0 for massive fields similarly to what was proved earlier for massless fields. (C) 2001 Published by Elsevier Science B.V.