Varying fine structure "constant" and charged black holes
  Speculation that the fine-structure constant $\alpha$ varies in spacetime has
a long history. We derive, in 4-D general relativity and in isotropic
coordinates, the solution for a charged spherical black hole according to the
framework for dynamical $\alpha$ (Bekenstein 1982). This solution coincides
with a previously known one-parameter extension of the dilatonic black hole
family. Among the notable properties of varying-$\alpha$ charged black holes
are adherence to a ``no hair'' principle, the absence of the inner (Cauchy)
horizon of the Reissner-Nordstrom black holes, the nonexistence of precisely
extremal black holes, and the appearance of naked singularities in an analytic
extension of the relevant metric. The exteriors of almost extremal electrically
(magnetically) charged black holes have simple structures which makes their
influence on applied magnetic (electric) fields transparent. We re-derive the
thermodynamic functions of the modified black holes; the otherwise difficult
calculation of the electric potential is done by a shortcut. We confirm that
variability of $\alpha$ in the wake of expansion of the universe does not
threaten the generalized second law
