Thermodynamics of 4D Dilatonic Black Holes and the Weak Gravity Conjecture

TL;DR

This paper investigates the weak gravity conjecture within 4D Einstein-Maxwell-dilaton black holes using thermodynamics, deriving corrected quantities and constraints on theory parameters to support the conjecture.

Contribution

It provides closed-form thermodynamic expressions for black holes with higher-derivative corrections and analyzes their implications for the weak gravity conjecture.

Findings

Corrected thermodynamic quantities derived explicitly.

Constraints on Wilson coefficients consistent with the conjecture.

Validation of the weak gravity conjecture in this context.

Abstract

Taking a thermodynamic perspective, we study the weak gravity conjecture in the context of 4D Einstein-Maxwell-dilaton theory. We find closed-form expressions for the corrected thermodynamic quantities in the presence of four-derivative terms in the action, and in particular the charge-to-mass ratio and entropy, for several families of solutions of special magnetic-to-electric charge ratio or dilaton coupling constant. Assuming that dyonic black holes themselves are the conjectured charged states, this places constraints on the Wilson coefficients of the theory which we show are satisfied under mild assumptions on the UV theory.