Varying fine structure "constant" and charged black holes

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

As accepted for Phys. Rev. D. 12 pages, RevTeX. Secs.II.A+B unified and simplified. Discussion in Sec.VIII of possible second law violation by cosmological alpha variability simplified, with new references. Abstract, Introduction and Summary updated

References in corpus (7)

• Phantom Black Holes in Einstein-Maxwell-Dilaton Theory
• Varying Constants
• Black holes in the TeVeS theory of gravity and their thermodynamics
• Time variation of fundamental couplings and dynamical dark energy
• Time variation of the fine structure constant in the early universe and the Bekenstein model
• Comment on "Black hole constraints on varying fundamental constants"
• Gravitational Effects of Varying Alpha Strings

Cited by in corpus (7)

• Varying constants, Gravitation and Cosmology
• Self-Calibration for 3-point Intrinsic Alignment Auto-Correlations in Weak Lensing Surveys
• Bouncing Anisotropic Universes with Varying Constants
• Redshifting of cosmological black bodies in BSBM varying-alpha theories
• Impact of inhomogeneities on slowly rolling Quintessence: implications for the local variations of the fine-structure constant
• Formation of a condensate during charged collapse
• Accelerated expansion as manifestation of gravity: when Dark Energy belongs to the left