Dilaton Black Holes Near the Horizon

TL;DR

This paper investigates the near-horizon geometries of supersymmetric dilaton black holes, revealing universal behaviors such as Robinson-Bertotti and linear dilaton vacua, and explores their supersymmetry properties and positivity bounds.

Contribution

It demonstrates that generic supersymmetric dilaton black holes tend to specific near-horizon geometries with enhanced supersymmetry, extending understanding of their structure and stability.

Findings

Near-horizon geometries are Robinson-Bertotti or 2D linear dilaton vacua.

Supersymmetry is enhanced near the horizon, with up to 8 unbroken supersymmetries.

Positivity bounds relate black hole mass to stringy 2D black hole properties.

Abstract

Generic $U(1)^2$ 4-d black holes with unbroken $N=1$ supersymmetry are shown to tend to a Robinson-Bertotti type geometry with a linear dilaton and doubling of unbroken supersymmetries near the horizon. Purely magnetic dilatonic black holes, which have unbroken $N=2$ supersymmetry, behave near the horizon as a 2-d linear dilaton vacuum $\otimes \, S^2$. This geometry is invariant under 8 supersymmetries, i.e. half of the original $N=4$ supersymmetries are unbroken. The supersymmetric positivity bound, which requires the mass of the 4-d dilaton black holes to be greater than or equal to the central charge, corresponds to positivity of mass for a class of stringy 2-d black holes.