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

Abstract

Starting from the Frolov-Zel'nikov stress-energy tensor 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 $S_q>0$, 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.

11 pages, REVTeX 3.0. To be published in Phys. Lett. B

Cited by in corpus (2)

• Casimir Effect in 2D Stringy Black Hole Backgrounds
• Entropy of quantum-corrected black holes