Mathematics – Mathematical Physics
Scientific paper
Sep 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998jmp....39.4608b&link_type=abstract
Journal of Mathematical Physics, Vol. 39, No. 9, p. 4608 - 4633
Mathematics
Mathematical Physics
Black Holes: Thermodynamics
Scientific paper
The author deals with some problems concerning quantum matter fields thermodynamics on static spherosymmetric black hole backgrounds. He studies the self-adjointness of the Euclidean wave operators relevant in the calculation of the partition function and of the thermal Green functions for the case of scalar quantum fields in thermal equilibrium with a Schwarzschild black hole. In this respect, the role of the horizon surface is analyzed. An approach to this topic is also discussed. It is found that, if the horizon surface is not included in the Euclidean manifold (or if it cannot be included, as in the case of a temperature different from the black hole one), essential self-adjointness is missing and boundary conditions on the horizon are required. The author also analyzes some qualitative spectral properties of the given wave operators after introducing an infrared regularization by means of a spherical box. He finds that in the standard Euclidean path integral approach the spectrum is purely discrete. The same analysis is carried out for the noncovariant choice of the functional measure in the Euclidean path integral. An analogous study is carried for an extremal Reissner-Nordström black hole and it is sketched in the nonextremal one. The latter is completely analogous to the Schwarzschild case, whereas in the extremal case it is found that the corresponding Riemannian manifold is complete for every choice of the temperature and that at finite four volume there is a nonvoid continuous spectrum. Physical implications of the results are discussed.
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