$E_{7(7)}$ invariant non-extremal entropy

TL;DR

This paper expresses the entropy of non-extremal black holes in supergravity models using U-duality invariants, extending previous results and proposing a generalization to broader supergravity theories.

Contribution

It introduces a formulation of non-extremal black hole entropy in terms of $E_{7(7)}$ invariants and extends the approach to $ ext{N}=8$ and $ ext{N}=2$ supergravity models.

Findings

Entropy expressed via $E_{7(7)}$ invariants.

Extension to $ ext{N}=8$ supergravity black holes.

Conjecture for $ ext{N}=2$ supergravity with cubic prepotential.

Abstract

The entropy of generic non-extremal dyonic black holes in the STU model has been shown to admit a remarkably universal form. The missing invariant in the formula was recently identified by S\'arosi using the formalism of quantum entanglement as well as a higher dimensional embedding of the U-duality group. Here, we express the non-extremal black hole entropy in the STU model in terms of U-duality covariant tensors. We then provide the extension to the most general non-extremal black hole of ungauged $\mathcal N= 8$ supergravity using $E_{7(7)}$ invariants. We also conjecture a generalization for ungauged $\mathcal N = 2$ supergravity coupled to vector multiplets with arbitrary cubic prepotential. The most general rotating dyonic black hole solution of the STU model with all scalar moduli turned on is provided in an appendix.