The vacuum polarization around an axionic stringy black hole

We consider the effect of vacuum polarization around the horizon of a four 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 ≫ (10^-15-10^-11)m_p (m_p is the proton mass), according to the assumed value of the axion mass (m_a{reversed tilde equals}10^-3-10^-6eV). 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.