Double-Horizon Limit and Decoupling of the Dynamics at the Horizon

TL;DR

This paper demonstrates that the double-horizon condition causes the decoupling of horizon dynamics from the rest of the spacetime, explaining the attractor mechanism in various black hole solutions.

Contribution

It establishes that the double-horizon leads to decoupled horizon equations, generalizing the attractor mechanism to rotating and non-rotating black holes in diverse gravity theories.

Findings

Horizon dynamics decouple from the bulk in double-horizon black holes.

The fields at the horizon satisfy differential equations in the angular coordinate.

The results apply to both Einstein and f(R) gravity theories, including with cosmological constant.

Abstract

We show that the attractor mechanism for generic black hole is a consequence of the double-horizon. Investigation of equations of motion shows that in the case of the double-horizon black holes, the dynamics of the geometry, the scalars and the gauge fields at the horizon decouples from the rest of the space. In the general case, the value of the fields at the horizon satisfies a number of differential equations of functions of the $\theta$ coordinate. We show this for the case of rotating and non-rotating electrically charged black holes in the general two derivative theories of gravity and f(R) gravities including the theories with cosmological constant.