Critical points of the Black-Hole potential for homogeneous special geometries

TL;DR

This paper extends the analysis of extremal black-hole attractor equations to homogeneous special geometries, revealing that non-BPS entropy formulas match symmetric cases, with deviations in non-homogeneous geometries linked to geometric data.

Contribution

It generalizes the attractor equation analysis to homogeneous coset spaces, providing new insights into entropy formulas for non-BPS black holes in these geometries.

Findings

Non-BPS entropy matches symmetric space results.

Deviations in non-homogeneous geometries depend on geometric data.

Entropy formula involves the central charge at critical points.

Abstract

We extend the analysis of N=2 extremal Black-Hole attractor equations to the case of special geometries based on homogeneous coset spaces. For non-BPS critical points (with non vanishing central charge) the (Bekenstein-Hawking) entropy formula is the same as for symmetric spaces, namely four times the square of the central charge evaluated at the critical point. For non homogeneous geometries the deviation from this formula is given in terms of geometrical data of special geometry in presence of a background symplectic charge vector.