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arXiv · 0707.1933

New attractor mechanism for spherically symmetric extremal black holes

Yun Soo Myung·Yong-Wan Kim·Young-Jai Park
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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 $V(ϕ)$. The condition of an attractor is given by $\nabla^2ϕ=V(ϕ_0)$ and $\bar{R}_2=-V^{\prime}(ϕ_0)$ and for a constant dilaton $ ϕ=ϕ_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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Yun Soo Myung, Yong-Wan Kim, Young-Jai Park. 2007-10-05. New attractor mechanism for spherically symmetric extremal black holes. https://doi.org/10.1103/physrevd.76.104045

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