Rotating Attractors

TL;DR

This paper demonstrates that the entropy and near horizon geometry of rotating extremal black holes in higher derivative gravity theories can be derived by extremizing an entropy function, revealing attractor behavior even with flat directions.

Contribution

It generalizes the entropy function formalism to rotating black holes in higher derivative theories, showing attractor behavior and independence from asymptotic moduli.

Findings

Entropy is obtained by extremizing a charge-dependent function.

Attractor behavior occurs when the entropy function has a unique extremum.

The entropy remains independent of asymptotic moduli even with flat directions.

Abstract

We prove that, in a general higher derivative theory of gravity coupled to abelian gauge fields and neutral scalar fields, the entropy and the near horizon background of a rotating extremal black hole is obtained by extremizing an entropy function which depends only on the parameters labeling the near horizon background and the electric and magnetic charges and angular momentum carried by the black hole. If the entropy function has a unique extremum then this extremum must be independent of the asymptotic values of the moduli scalar fields and the solution exhibits attractor behaviour. If the entropy function has flat directions then the near horizon background is not uniquely determined by the extremization equations and could depend on the asymptotic data on the moduli fields, but the value of the entropy is still independent of this asymptotic data. We illustrate these results in the context of two derivative theories of gravity in several examples. These include Kerr black hole, Kerr-Newman black hole, black holes in Kaluza-Klein theory, and black holes in toroidally compactified heterotic string theory.