The vacuum polarization around an axionic stringy black hole

TL;DR

This paper investigates vacuum polarization effects around axionic stringy black holes, identifying mass bounds for avoiding polarization and conditions under which the vacuum is always polarized, depending on black hole charge and stability.

Contribution

It provides new insights into vacuum polarization near axionic black holes, especially in extreme and nondegenerate charge limits, with implications for black hole mass bounds and stability.

Findings

Lower mass limit for avoiding polarization: M >> 10^{-15} to 10^{-11} m_p.

No upper mass bounds due to lack of thermal radiation in the extremal limit.

Vacuum always polarizes in the nondegenerate, classically unstable limit unless the cosmological constant diverges.

Abstract

We consider the effect of vacuum polarization around the horizon of a 4 dimensional axionic stringy black hole. In the extreme degenerate limit ($Q_a=M$), the lower limit on the black hole mass for avoiding the polarization of the surrounding medium is $M\gg (10^{-15}\div 10^{-11})m_p$ ($m_p$ is the proton mass), according to the assumed value of the axion mass ($m_a\simeq (10^{-3}\div 10^{-6})~eV$). In this case, there are no upper bounds on the mass due to the absence of the thermal radiation by the black hole. In the nondegenerate (classically unstable) limit ($Q_a<M$), the black hole always polarizes the surrounding vacuum, unless the effective cosmological constant of the effective stringy action diverges.