Black hole thermodynamics at 4 derivatives, natural variables and BPS limits

TL;DR

This paper investigates higher-derivative corrections to black hole thermodynamics in Einstein-Maxwell theory across dimensions, introducing natural variables, exploring BPS limits, and clarifying discrepancies in supergravity localization results.

Contribution

It extends black hole thermodynamics analysis to include all four-derivative couplings, introduces natural variables for simplification, and identifies a new BPS-like limit in four dimensions.

Findings

Computed first-order thermodynamic corrections for static and rotating black holes in D=4 and D=5.

Recast on-shell actions using left- and right-moving chemical potentials for simplification.

Identified a novel BPS-like limit in D=4 and verified BPS thermodynamics in D=5.

Abstract

We study Einstein-Maxwell theory in $D \geq 3$ spacetime dimensions including all Lorentz-invariant parity-even four-derivative couplings. Building on the results of arXiv:2312.11610, we consider static, charged, asymptotically flat black hole solutions to first order in the higher-derivative expansion. In $D=4$ and $D=5$, we compute the corrected black hole thermodynamics and compare with the Reall-Santos prescription based on the two-derivative background, highlighting a subtlety when both inner and outer horizons are involved. By introducing natural variables, as in arXiv:2304.07320, we recast the on-shell actions in terms of left- and right-moving chemical potentials, which significantly simplifies the analysis. We also compute first-order thermodynamic corrections for the most general rotating black holes in $D=4$ and $D=5$, without modifying the background solutions. We identify a novel BPS-like limit in $D=4$, extending known supergravity results beyond their traditional domain of validity. Finally, in $D=5$, the analysis of BPS and almost BPS limits enables an independent verification of the five-dimensional BPS thermodynamics. We clarify the origin of a discrepancy in the literature concerning higher-derivative supergravity localization, sharpening the tension between direct computations and predictions based on the $D=4$/$D=5$ connection.