Entropies of Scalar Fields on Three Dimensional Black Holes

Details Entropies of Scalar Fields on Three Dimensional Black Holes Entropies of Scalar Fields on Three Dimensional Black Holes

1994-12-16

arxiv.org/abs/hep-th/9412144v2

Nucl.Phys.B447:340-372,1995

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, Latex, 1 figure, postscript file attached at the end

Scientific paper

10.1016/0550-3213(95)00197-Z

Thermodynamics of scalar fields is investigated in three dimensional black hole backgrounds in two approaches. One is mode expansion and direct computation of the partition sum, and the other is the Euclidean path integral approach. We obtain a number of exact results, for example, mode functions, Hartle-Hawking Green functions on the black holes, Green functions on a cone geometry, free energies and entropies. They constitute reliable bases for the thermodynamics of scalar fields. It is shown that thermodynamic quantities largely depend upon the approach to calculate them, boundary conditions for the scalar fields and regularization method. We find that, in general, the entropies are not proportional to the area of the horizon and that their divergent parts are not necessarily due to the existence of the horizon.

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