Killing approximation for vacuum and thermal stress-energy tensor in static space-times

Details Killing approximation for vacuum and thermal stress-energy tensor in static space-times Killing approximation for vacuum and thermal stress-energy tensor in static space-times

May 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phrvd..35.3031f&link_type=abstract

Physical Review D (Particles and Fields), Volume 35, Issue 10, 15 May 1987, pp.3031-3044

Physics

73

Theory Of Quantized Fields, Black Holes

Scientific paper

The problem of the vacuum polarization of conformal massless fields in static space-times is considered. A tensor Tμν constructed from the curvature, the Killing vector, and their covariant derivatives is proposed which can be used to approximate the average value of the stress-energy tensor ren in such spaces. It is shown that if (i) its trace T ɛɛ coincides with the trace anomaly ren, (ii) it satisfies the conservation law Tμɛ ɛ=0, and (iii) it has the correct behavior under the scale transformations, then it is uniquely defined up to a few arbitrary constants. These constants must be chosen to satisfy the boundary conditions. In the case of a static black hole in a vacuum these conditions single out the unique tensor Tμν which provides a good approximation for ren in the Hartle-Hawking vacuum. The relation between this approach and the Page-Brown-Ottewill approach is discussed.

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