Hiroko Koyama — Page 2

arXiv2000

Vacuum Polarization of Massive Scalar Fields on the Black Hole Horizon

Vacuum polarization of massive scalar fields in a thermal state at arbitrary temperature is studied near the horizon of a Reissner-Nordström black hole. We derived an analytic form of $<ϕ^2>$ 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.

gr-qc↗

arXiv2000

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

We 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.

gr-qc↗