Varying fine structure "constant" and charged black holes

TL;DR

This paper derives solutions for charged black holes with a varying fine-structure constant in general relativity, revealing unique properties like absence of inner horizons and naked singularities, and confirms thermodynamic consistency with a changing $\alpha$.

Contribution

It provides the first explicit solution for charged black holes with a dynamical fine-structure constant in 4-D GR, extending previous models and analyzing their properties.

Findings

Charged black holes with varying $\alpha$ obey a no-hair principle.

Such black holes lack inner (Cauchy) horizons.

The solutions include naked singularities and modified thermodynamics.

Abstract

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