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

Journal Article · Fri May 15 00:00:00 EDT 1987 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.35.3031· OSTI ID:5973710

Frolov, V P; Zel'nikov, A I

The problem of the vacuum polarization of conformal massless fields in static space-times is considered. A tensor T/sub ..mu..//sub ..nu../ 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 /sup ren/ in such spaces. It is shown that if (i) its trace T /sub epsilon//sup epsilon/ coincides with the trace anomaly /sup ren/, (ii) it satisfies the conservation law T/sup ..mu..//sup epsilon/ /sub ;//sub epsilon/ = 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 T/sub ..mu..//sub ..nu../ which provides a good approximation for /sup ren/ in the Hartle-Hawking vacuum. The relation between this approach and the Page-Brown-Ottewill approach is discussed.

• Research Organization: Department of Physics, University of British Columbia, Vancouver, British Columbia, Canada V6T 2A6 and P.N. Lebedev Physical Institute, Leninsky Prospect 53, Moscow 117924, Union of Soviet Socialist Republics
• OSTI ID: 5973710
• Journal Information: Phys. Rev. D; (United States), Vol. 35:10
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
VACUUM POLARIZATION
SPACE-TIME
BLACK HOLES
BOUNDARY CONDITIONS
GRAVITATIONAL FIELDS
GREEN FUNCTION
MASSLESS PARTICLES
RENORMALIZATION
SCALAR FIELDS
TENSORS
ELEMENTARY PARTICLES
FUNCTIONS
657003* - Theoretical & Mathematical Physics- Relativity & Gravitation