New attractor mechanism for spherically symmetric extremal black holes

TL;DR

This paper proposes a new attractor mechanism using 2D dilaton gravity to accurately compute the entropy of spherically symmetric extremal black holes, including regular black holes from nonlinear electrodynamics.

Contribution

It introduces a novel attractor method based on 2D dilaton gravity that effectively determines black hole entropy where previous entropy function approaches fail.

Findings

Successfully recovers Bekenstein-Hawking entropy for extremal regular black holes.

Demonstrates the new method's effectiveness over the entropy function approach.

Provides a concrete example with Einstein gravity coupled to nonlinear electrodynamics.

Abstract

We introduce a new attractor mechanism to find the entropy for spherically symmetric extremal black holes. The key ingredient is to find a two-dimensional (2D) dilaton gravity with the dilaton potential $V(\phi)$. The condition of an attractor is given by $\nabla^2\phi=V(\phi_0)$ and $\bar{R}_2=-V^{\prime}(\phi_0)$ and for a constant dilaton $ \phi=\phi_0$, these are also used to find the location of the degenerate horizon $r=r_{e}$ of an extremal black hole. As a nontrivial example, we consider an extremal regular black hole obtained from the coupled system of Einstein gravity and nonlinear electrodynamics. The desired Bekenstein-Hawking entropy is successfully recovered from the generalized entropy formula combined with the 2D dilaton gravity, while the entropy function approach does not work for obtaining this entropy.