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

Abstract

We study vacuum polarization of quantized massive scalar fields $\varphi$ 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 $<{\varphi }^2{>}_H$ at the event horizon with the area $4\pi r_{+}^2$. It is confirmed that the polarization amplitude $<{\varphi }^2{>}_H$ is free from any divergence due to the infinite red-shift effect. Our main purpose is to clarify the dependence of $<{\varphi }^2{>}_H$ on field mass $m$ in relation to the excitation mechanism. It is shown for small-mass fields with $m{r}_{+}\ll 1$ how the excitation of $<{\varphi }^2{>}_H$ caused by finite black-hole temperature is suppressed as $m$ increases, and it is verified for very massive fields with $m{r}_{+}\gg 1$ that $<{\varphi }^2{>}_H$ 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 $m{r}_{+}\simeq 0.38$ 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.

24 pages, 1 figure Accepted in PRD

References in corpus (1)

• Semiclassical charged black holes with a quantized massive scalar field

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