Statistical entropies of scalar and spinor fields in Vaidya-de Sitter space-time computed by the thin-layer method

Details Statistical entropies of scalar and spinor fields in Vaidya-de Sitter space-time computed by the thin-layer method Statistical entropies of scalar and spinor fields in Vaidya-de Sitter space-time computed by the thin-layer method

Aug 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001phrvd..64d4025h&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 64, Issue 4, August 15, 2001, id.044025

Mathematics

Logic

38

Quantum Aspects Of Black Holes, Evaporation, Thermodynamics, Quantum Field Theory In Curved Spacetime, Black Holes

Scientific paper

The brick-wall method based on thermal equilibrium at a large scale cannot be applied to cases out of equilibrium, such as nonstationary space-time with two horizons, for example, Vaidya-de Sitter space-time. We improve the brick-wall method and propose a thin-layer method. The entropies of scalar and spinor fields in Vaidya-de Sitter space-time are calculated by the thin-layer method. The condition of local equilibrium near the two horizons is used as a working postulate and is maintained for a black hole which evaporates slowly enough and whose mass is far greater than the Planck scale. There are two horizons in Vaidya-de Sitter space-time. We think that the total entropy is mainly attributed to the two layers near the two horizons. The entropy of a scalar field in Vaidya-de Sitter space-time is a linear sum of the area of the black hole horizon and that of the cosmological horizon. Thinking of Dirac equations in the Newman-Penrose formalism, there are four components of the wave functions F1, F2, G1, and G2. The total entropy is summed up from the entropies corresponding to the four components. On the same condition of the scalar field, the resulting entropy is 7/2 times that of the scalar field, and is also a linear sum of the area of the black hole horizon and that of the cosmological horizon. The difference from the stationary black hole is that the result relies on time-dependent cutoffs.

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