The Non-BPS Black Hole Attractor Equation

TL;DR

This paper derives the non-supersymmetric attractor equation for extremal non-BPS black holes, explaining the stabilization of moduli at the horizon and analyzing specific solutions in string theory compactifications.

Contribution

It provides a detailed derivation of the non-BPS attractor equation and explores moduli stabilization in non-supersymmetric black holes within string theory.

Findings

Derived the non-supersymmetric attractor equation.

Showed moduli are fixed at critical points of the black hole potential.

Analyzed solutions in Calabi-Yau compactifications.

Abstract

We study the attractor mechanism for extremal non-BPS black holes with an infinite throat near horizon geometry, developing, as we do so, a physical argument as to why such a mechanism does not exist in non-extremal cases. We present a detailed derivation of the non-supersymmetric attractor equation. This equation defines the stabilization of moduli near the black hole horizon: the fixed moduli take values specified by electric and magnetic charges corresponding to the fluxes in a Calabi Yau compactification of string theory. They also define the so-called double-extremal solutions. In some examples, studied previously by Tripathy and Trivedi, we solve the equation and show that the moduli are fixed at values which may also be derived from the critical points of the black hole potential.