Extremal non-BPS black holes and entropy extremization

TL;DR

This paper investigates extremal non-BPS black holes in N=2 supergravity, comparing attractor equations and entropy extremization, revealing distinct behaviors near the conifold point and analyzing stability and entropy maxima.

Contribution

It provides explicit solutions to attractor equations for a conifold-related prepotential, highlighting differences between supersymmetric and non-supersymmetric cases.

Findings

Non-supersymmetric solutions behave differently near the conifold point.

The entropy maximum for non-BPS solutions does not coincide with the conifold point.

Stability analysis shows distinct attractor regions for non-BPS black holes.

Abstract

At the horizon, a static extremal black hole solution in N=2 supergravity in four dimensions is determined by a set of so-called attractor equations which, in the absence of higher-curvature interactions, can be derived as extremization conditions for the black hole potential or, equivalently, for the entropy function. We contrast both methods by explicitly solving the attractor equations for a one-modulus prepotential associated with the conifold. We find that near the conifold point, the non-supersymmetric solution has a substantially different behavior than the supersymmetric solution. We analyze the stability of the solutions and the extrema of the resulting entropy as a function of the modulus. For the non-BPS solution the region of attractivity and the maximum of the entropy do not coincide with the conifold point.