Thermal stress tensors in static Einstein spaces

Journal Article · Mon Mar 15 00:00:00 EST 1982 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.25.1499· OSTI ID:5420053

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The Bekenstein-Parker Gaussian path-integral approximation is used to evaluate the thermal propagator for a conformally invariant scalar field in an ultrastatic metric. If the ultrastatic metric is conformal to a static Einstein metric, the trace anomaly vanishes and the Gaussian approximation is especially good. One then gets the ordinary flat-space expressions for the renormalized mean squared field and stress-energy tensor in the ultrastatic metric. Explicit formulas for the changes in and resulting from a conformal transformation of an arbitrary metric are found and used to take the Gaussian approximations for these quantities in the ultrastatic metric over to the Einstein metric. The result for is exact for de Sitter space and agrees closely with the numerical calculations of Fawcett and Whiting in the Schwarzschild metric. The result for is exact in de Sitter space and the Nariai metric and is close to Candelas's values on the bifurcation two-sphere in the Schwarzschild metric. Thus one gets a good closed-form approximation for the energy density and stresses of a conformal scalar field in the Hartle-Hawking state everywhere outside a static black hole.

• Research Organization: Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802
• OSTI ID: 5420053
• Journal Information: Phys. Rev. D; (United States), Vol. 25:6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BLACK HOLES
THERMAL RADIATION
SCALAR FIELDS
PROPAGATOR
CONFORMAL INVARIANCE
DE SITTER GROUP
KERNELS
METRICS
RENORMALIZATION
ELECTROMAGNETIC RADIATION
INVARIANCE PRINCIPLES
LIE GROUPS
RADIATIONS
SYMMETRY GROUPS
657003* - Theoretical & Mathematical Physics- Relativity & Gravitation