Black holes, first-order flow equations and geodesics on symmetric spaces

TL;DR

This paper derives first-order flow equations for spherically symmetric black holes with scalars and vectors, focusing on theories with symmetric moduli spaces, and discusses conditions for the existence of such flows.

Contribution

It provides a general form of gradient flow equations for black holes in theories with symmetric moduli spaces, extending previous results.

Findings

Derived first-order flow equations for extremal and non-extremal black holes

Identified conditions for the existence of gradient flows in symmetric moduli space theories

Reviewed and summarized previous results on black hole flow equations

Abstract

For both extremal and non-extremal spherically symmetric black holes in theories with massless scalars and vectors coupled to gravity, we derive a general form of first-order gradient flow equations, equivalent to the equations of motion. For theories that have a symmetric moduli space after a dimensional reduction over the timelike direction, we discuss the condition for such a gradient flow to exist. This note reviews the results of arXiv:0810.1528 [hep-th].