2000/02/04 by Akira Tomimatsu, Hiroko Koyama · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum Electrodynamics and Casimir Effect #gr-qc
paper · pdf · doi:10.1103/physrevd.61.124010
published as Phys.Rev. D61 (2000) 124010 · 24 pages, 1 figure Accepted in PRD
arxiv created 2000/02/04 · openalex publication_date 2000/05/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study vacuum polarization of quantized massive scalar fields \ensuremathφ in equilibrium at the black-hole temperature in a Reissner-Nordstr"om background. By means of the Euclidean space Green's function we analytically derive the renormalized expression 〈\ensuremathφ2〉H at the event horizon with the area 4\ensuremathπr+2. It is confirmed that the polarization amplitude 〈\ensuremathφ2〉H is free from any divergence due to the infinite redshift effect. Our main purpose is to clarify the dependence of 〈\ensuremathφ2〉H on the field mass m in relation to the excitation mechanism. It is shown for small-mass fields with mr+\ensuremath≪1 how the excitation of 〈\ensuremathφ2〉H caused by a finite black-hole temperature is suppressed as m increases, and it is verified for very massive fields with mr+\ensuremath≫1 that 〈\ensuremathφ2〉H decreases in proportion to m^\ensuremath-2 with an amplitude equal to the DeWitt-Schwinger approximation. In particular, we find a resonance behavior with a peak amplitude at mr+\ensuremath≃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.