New attractor mechanism for spherically symmetric extremal black holes

Details New attractor mechanism for spherically symmetric extremal black holes New attractor mechanism for spherically symmetric extremal black holes

2007-07-13

arxiv.org/abs/0707.1933v2

Phys.Rev.D76:104045,2007

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, 4 figures, Accepted for publication in Physical Review D. This version includes revisions suggested by the referee

Scientific paper

10.1103/PhysRevD.76.104045

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.

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