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Abstract: We introduce a new attractor mechanism to find the entropy for sphericallysymmetric extremal black holes. The key ingredient is to find a two-dimensional2D dilaton gravity with the dilaton potential $V\phi$. The condition of anattractor is given by $ abla^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 $r=r {e}$ ofan extremal black hole. As a nontrivial example, we consider an extremalregular black hole obtained from the coupled system of Einstein gravity andnonlinear electrodynamics. The desired Bekenstein-Hawking entropy issuccessfully recovered from the generalized entropy formula combined with the2D dilaton gravity, while the entropy function approach does not work forobtaining this entropy.



Autor: Yun Soo Myung, Yong-Wan Kim, Young-Jai Park

Fuente: https://arxiv.org/







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