Derivative Corrections to Extremal Black Holes with Moduli

TL;DR

This paper provides formulas for calculating leading corrections to mass, entropy, and self-force of extremal black holes with moduli due to higher-derivative operators, applicable to static, spherically symmetric solutions.

Contribution

It introduces a method to compute these corrections without solving the full equations of motion, linking higher-derivative couplings to black hole properties and swampland conjectures.

Findings

Formulas for mass, entropy, and self-force corrections derived.

Corrections depend linearly on higher-derivative couplings.

Applicable to black holes with arbitrary gauge and moduli couplings.

Abstract

We derive formulas for the leading mass, entropy, and long-range self-force corrections to extremal black holes due to higher-derivative operators. These formulas hold for black holes with arbitrary couplings to gauge fields and moduli, provided that the leading-order solutions are static, spherically-symmetric, extremal, and have nonzero horizon area. To use these formulas, both the leading-order black hole solution and the higher-derivative effective action must be known, but there is no need to solve the derivative-corrected equations of motion. We demonstrate that the mass, entropy and self-force corrections involve linearly-independent combinations of the higher-derivative couplings at any given point in the moduli space, and comment on their relations to various swampland conjectures.