  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.
