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 AdS2×S2. 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.
Highlights
Growing interest in the extremal black holes is motivated by their unusual and not fully understood nature
We investigate whether the entropy function approach does work for deriving the entropy of a magnetically charged extremal regular black hole without singularity
We show that the entropy function approach proposed by Sen does not lead to a correct form of the Bekenstein-Hawking entropy of an extremal Regular black holes (RBHs)
Summary
Growing interest in the extremal black holes is motivated by their unusual and not fully understood nature. Matyjasek investigated the magnetically charged extremal RBH with the near horizon geometry of AdS2 × S2 and its relation with the exact solutions of the Einstein field equations [12, 13]. This type of RBHs can be employed to test whether the entropy function approach is or not suitable for obtaining the entropy of the extremal RBHs. On the other hand, string theory suggests that higher curvature terms can be added to the Einstein gravity [14]. Using the generalized entropy formula based on Wald’s Noether charge formalism [25], we find the correct entropy
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
