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

O. B. Zaslavskii
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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 $%s=1/2$ $S_{q}>0$, 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.

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O. B. Zaslavskii. 2001-01-14. Entropy of massive fields near a black hole and vacuum polarization: thermodynamics without statistical mechanics. https://doi.org/10.1016/s0370-2693(01)00148-4

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