Vacuum polarization in Schwarzschild spacetime

Journal Article · Tue Apr 15 04:00:00 EST 1980 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.21.2185· OSTI ID:5447764

Candelas, P

The polarization of the vacuum induced by gravitation is studied for massless fields in the region exterior to the horizon of a Schwarzschild black hole. The renormalized value of < phi/sup 2/(x) > is calculated according to the ''covariant point-separation scheme'' for each of the Boulware, Hartle-Hawking, and Unruh ''vacua.'' The form of the renormalized expectation value of the stress tensor near the horizon and at infinity is discussed for each of these three states. It is found that the Unruh vacuum best approximates the state that would obtain following the gravitational collapse of a massive body in the sense that the expectation values of physical observables are finite, in a freely falling frame, on the future horizon and that this state is empty near infinity apart from an outgoing flux of a blackbody radiation. The response of an Unruh box is examined further in the light of the results obtained for the stress tensor. Finally it is shown by explicit solution of the linearized Einstein equations that the area of the horizon decreases at the rate expected from the flux at infinity.

• Research Organization: Center for Theoretical Physics, University of Texas at Austin, Austin, Texas 78712
• OSTI ID: 5447764
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 21:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
BLACKBODY RADIATION
EINSTEIN FIELD EQUATIONS
ELECTROMAGNETIC RADIATION
ELEMENTARY PARTICLES
EQUATIONS
EXPECTATION VALUE
FIELD EQUATIONS
FIELD THEORIES
GRAVITATIONAL COLLAPSE
MASSLESS PARTICLES
METRICS
QUANTUM FIELD THEORY
RADIATIONS
RENORMALIZATION
SCHWARZSCHILD METRIC
SCHWARZSCHILD RADIUS
SPACE-TIME
TENSOR FORCES
VACUUM POLARIZATION