Causality Constraints on Black Hole Thermodynamics in Nonlinear Electrodynamics

TL;DR

This paper investigates how causality constraints in nonlinear electrodynamics influence black hole thermodynamics, revealing new monotonicity properties of black hole parameters that extend previous entropy positivity results.

Contribution

It establishes causality constraints on black hole thermodynamics in nonlinear electrodynamics, demonstrating new monotonicity properties of black hole ratios that generalize earlier entropy positivity findings.

Findings

Mass-to-charge ratio of extremal black holes is monotonic.

Entropy-to-mass-squared ratio decreases monotonically with mass.

Results extend positivity of entropy corrections to all orders in nonlinear electrodynamics.

Abstract

We study causality constraints on black hole thermodynamics in nonlinear electrodynamics, where the Lagrangian is taken to be an arbitrary function of the electromagnetic field strength tensor. By requiring the absence of superluminal propagation, we show that the mass-to-charge ratio of extremal black holes exhibits a certain monotonicity previously studied in the context of the weak gravity conjecture. Furthermore, under the same condition, we demonstrate that the entropy-to-mass-squared ratio of black holes, which we interpret as an entropy density, decreases monotonically with increasing mass, while keeping the mass-to-charge ratio fixed. This new monotonicity property extends previous studies on the positivity of four-derivative corrections to black hole entropy in the microcanonical ensemble to all orders in nonlinear electrodynamics.