Entropy of an extremal regular black hole

Abstract

We introduce a magnetically charged extremal regular black hole in the coupled system of Einstein gravity and nonlinear electrodynamics. Its near horizon geometry is given by $Ad{S}_2\times S^2$. It turns out that the entropy function approach does not automatically lead to a correct entropy of the Bekenstein-Hawking entropy. This contrasts to the case of the extremal Reissner-Norström black hole in the Einstein-Maxwell theory. We conclude that the entropy function approach does not work for a magnetically charged extremal regular black hole without singularity, because of the nonlinearity of the entropy function.

17 Pages, 4 figures, version to appear in Phys. Lett. B

References in corpus (3)

• Quantum Cooling Evaporation Process in Regular Black Holes
• Exactly Soluble BPS Black Holes in Higher Curvature N=2 Supergravity
• On the Entropy Function and the Attractor Mechanism for Spherically Symmetric Extremal Black Holes

Cited by in corpus (6)

• Entropy of the Schwarzschild black hole to all orders in the Planck length
• Stationary black holes and attractor mechanism
• Thermodynamics of Einstein-Born-Infeld black holes in three dimensions
• New attractor mechanism for spherically symmetric extremal black holes
• Entropy of nonlinear black holes in quadratic gravity
• A note on non-linear electrodynamics, regular black holes and the entropy function