Nilpotent orbits in real symmetric pairs and stationary black holes

TL;DR

This paper classifies nilpotent orbits in real symmetric pairs, crucial for understanding stationary solutions in supergravity models, by developing methods and applying them to classify solutions in the STU-supergravity model.

Contribution

It introduces two approaches for classifying nilpotent orbits in real symmetric pairs and applies them to classify solutions in a specific supergravity model.

Findings

Classified nilpotent orbits of SL_2(R)^4 acting on tensor powers.

Enabled classification of all stationary solutions in the STU-supergravity model.

Provided explicit examples illustrating the orbit classification methods.

Abstract

In the classification of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In this paper we discuss two approaches to determining the nilpotent orbits of a real symmetric pair. We apply our methods to an explicit example, and thereby classify the nilpotent orbits of SL_2(R)^4 acting on the fourth tensor power of the natural 2-dimensional SL_2(R)-module. This makes it possible to classify all stationary solutions of the so-called STU-supergravity model.