Varying Fine Structure Constant and Black Hole Physics

TL;DR

This paper explores the implications of a slowly varying fine structure constant on black hole physics, demonstrating that such variations are adiabatic and consistent with thermodynamics, while constraining black hole properties.

Contribution

It provides a model-independent analysis of adiabatic variations in the fine structure constant and their effects on charged black holes, including thermodynamic consistency and parameter constraints.

Findings

Black hole second law remains valid under alpha variation

Constraints on black hole charge and mass due to alpha change

Estimated work done on black holes from alpha variation

Abstract

Recent astrophysical observations suggest that the value of fine structure constant $\alpha=e^2/\hbar c$ may be slowly increasing with time. This may be due to an increase of $e$ or a decrease of $c$, or both. In this article, we argue from model independent considerations that this variation should be considered adiabatic. Then, we examine in detail the consequences of such an adiabatic variation in the context of a specific model of quantized charged black holes. We find that the second law of black hole thermodynamics is obeyed, regardless of the origin of the variation, and that interesting constraints arise on the charge and mass of black holes. Finally, we estimate the work done on a black hole of mass $M$ due to the proposed $\alpha$ variation.