Vacuum polarization in the Schwarzschild spacetime and dimensional reduction

Abstract

A massless scalar field minimally coupled to gravity and propagating in the Schwarzschild spacetime is considered. After dimensional reduction under spherical symmetry the resulting 2D field theory is canonically quantized and the renormalized expectation values $<T_{ab}>$ of the relevant energy-momentum tensor operator are investigated. Asymptotic behaviours and analytical approximations are given for $<T_{ab}>$ in the Boulware, Unruh and Hartle-Hawking states. Special attention is devoted to the black-hole horizon region where the WKB approximation breaks down.

LaTeX (revtex), 13 pages, address and some minor misprints corrected

References in corpus (10)

• On 4D-Hawing Radiation from Effective Action
• Hawking radiation from dilaton gravity in 1 + 1 dimensions: a pedagogical review
• Hawking radiation by effective two-dimensional theories
• The Dimensional-Reduction Anomaly
• Effective action and Hawking radiation for dilaton coupled scalars in two dimensions
• 4D quantum black hole physics from 2D models?
• Quantum corrections for (anti)-evaporating black hole
• The Dimensional-Reduction Anomaly in Spherically Symmetric Spacetimes
• Vacuum Polarization of Massive Scalar Fields on the Black Hole Horizon
• Vacuum polarization of scalar fields near Reissner-Nordström black holes and the resonance behavior in field-mass dependence

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