Partition function of non-supersymmetric black holes in the supergravity limit

TL;DR

This paper proposes a formula for the free energy of non-supersymmetric black hole attractors in type IIA(B) superstring theory within the supergravity limit, extending the understanding of black hole thermodynamics beyond supersymmetric cases.

Contribution

It introduces a new expression for the free energy of non-supersymmetric black holes and proposes a mixed ensemble framework for these objects in supergravity.

Findings

Derived the free energy for non-supersymmetric black hole attractors.

Identified the free energy differs from BPS cases by a factor of 4.

Proposed a mixed ensemble approach for non-supersymmetric black holes.

Abstract

In this note, we propose the free energy of general \emph{non-supersymmetric} black hole attractors arising in type IIA(B) superstrings on 3-fold Calabi-Yau, in the supergravity limit. This, by definition, differs from its counterpart BPS free energy by a factor of $4 $. Correspondingly, a mixed ensemble for these black holes is proposed.