New attractor mechanism for spherically symmetric extremal black holes

Understand

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.