Black Holes and Critical Points in Moduli Space

TL;DR

This paper investigates the stabilization of scalar fields near supersymmetric black hole horizons, analyzing critical points of a potential within special geometry and relating it to thermodynamic metrics and critical phenomena.

Contribution

It introduces a geometric framework for understanding scalar stabilization at black hole horizons using special geometry and thermodynamic metrics.

Findings

Extremal central charge minimizes BPS mass and potential at positive moduli space metric.

Critical points correspond to stable scalar configurations near black hole horizons.

Connections established between black hole physics and thermodynamic geometric approaches.

Abstract

We study the stabilization of scalars near a supersymmetric black hole horizon using the equation of motion of a particle moving in a potential and background metric. When the relevant 4-dimensional theory is described by special geometry, the generic properties of the critical points of this potential can be studied. We find that the extremal value of the central charge provides the minimal value of the BPS mass and of the potential under the condition that the moduli space metric is positive at the critical point. We relate these ideas to the Weinhold and Ruppeiner metrics introduced in the geometric approach to thermodynamics and used for study of critical phenomena.