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Vacuum Polarization of Massive Scalar Fields on the Black Hole Horizon

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arxiv gr-qc/0003078 v1 pith:BOZX7Z74 submitted 2000-03-20 gr-qc

classification gr-qc
keywords horizonblackholepolarizationvacuumnearscalartemperature
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abstract

Vacuum polarization of massive scalar fields in a thermal state at arbitrary temperature is studied near the horizon of a Reissner-Nordstr\"{o}m black hole. We derived an analytic form of $<\phi^2>$ approximately in the large mass limit near the black hole horizon. We uses the zeroth order WKB approximation and power series expansion near the horizon for the Euclideanized mode function. Our formula for the vacuum polarization shows regular behavior on the horizon if the temperature of the scalar field is equal to the Hawking temperature of the black hole. The finite part of the vacuum polarization agrees with the result of the DeWitt-Schwinger approximation up to $O(m^{-4})$ which is the next leading order of the expansion.

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  1. Black holes in f(R) theory of gravity with compact extra dimensions

    gr-qc 2026-07 conditional novelty 5.0 of 10

    In D=4+n f(R) gravity with a constant-radius extra n-sphere, vacuum polarization of nonminimally coupled fields yields an asymptotically flat 4D Schwarzschild solution whose extra-radius is set by the quantum stress-t...

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