Vacuum polarization of scalar fields near Reissner-Nordström black holes and the resonance behavior in field-mass dependence

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dc.creatorTomimatsu, Akira
dc.creatorKoyama, Hiroko
dc.date2000-02-04
dc.date.accessioned2026-07-07T08:33:21Z
dc.date.available2026-07-07T08:33:21Z
dc.descriptionWe study vacuum polarization of quantized massive scalar fields $ϕ$ in equilibrium at black-hole temperature in Reissner-Nordström background. By means of the Euclidean space Green's function we analytically derive the renormalized expression $<ϕ^{2}>_{H}$ at the event horizon with the area $4πr_{+}^{2}$. It is confirmed that the polarization amplitude $<ϕ^{2}>_{H}$ is free from any divergence due to the infinite red-shift effect. Our main purpose is to clarify the dependence of $<ϕ^{2}>_{H}$ on field mass $m$ in relation to the excitation mechanism. It is shown for small-mass fields with $mr_{+}\ll1$ how the excitation of $<ϕ^{2}>_{H}$ caused by finite black-hole temperature is suppressed as $m$ increases, and it is verified for very massive fields with $mr_{+}\gg1$ that $<ϕ^{2}>_{H}$ decreases in proportion to $m^{-2}$ with the amplitude equal to the DeWitt-Schwinger approximation. In particular, we find a resonance behavior with a peak amplitude at $mr_{+}\simeq 0.38$ in the field-mass dependence of vacuum polarization around nearly extreme (low-temperature) black holes. The difference between Scwarzschild and nearly extreme black holes is discussed in terms of the mass spectrum of quantum fields dominant near the event horizon.
dc.description24 pages, 1 figure Accepted in PRD
dc.identifierhttps://arxiv.org/abs/gr-qc/0002020
dc.identifierhttp://arxiv.org/abs/gr-qc/0002020
dc.identifierPhys.Rev. D61 (2000) 124010
dc.identifierdoi:10.1103/PhysRevD.61.124010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139100
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleVacuum polarization of scalar fields near Reissner-Nordström black holes and the resonance behavior in field-mass dependence
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