Entropy of non-extremal STU black holes: the F-invariant unveiled

TL;DR

This paper derives a U-duality invariant formula for the entropy of general non-extremal STU black holes, expressed in terms of asymptotic charges, and discusses its reduction to known cases and potential generalization to maximal supergravity.

Contribution

It provides the first manifestly U-duality invariant entropy formula for non-extremal STU black holes in terms of asymptotic charges.

Findings

Derived a U-duality invariant entropy formula for non-extremal STU black holes.

Reduced the formula to known solutions like the Kaluza-Klein black hole.

Discussed extension to E7(7) invariance in maximal supergravity.

Abstract

We find a manifestly U-duality invariant formula for the Bekenstein-Hawking entropy of the most general 4 dimensional, stationary, asymptoticaly flat, non-extremal STU black holes constructed recently by Chow and Comp\`ere. The expression is entirely in terms of asymptotic charges. It involves the "scalar charges" of the black hole which still need to be solved in terms of the dyonic charges and the mass. We discuss how the formula reduces to some of the known results as the Klauza-Klein black hole and the dilute gas limit of Cveti\v{c} and Larsen. We give the expected generalization to an $E_{7(7)}$ invariant in the case of maximal $\mathcal{N}=8$ supergravity.