C S Lopez-Monsalvo, F Nettel, H Quevedo
The thermodynamics of dirty (Maxwell-Dilaton) black holes has been extensively studied. It has served as a fertile ground to test ideas about temperature through various definitions of surface gravity. In this paper, we make an independent analysis of this black hole solution in both, Einstein and Jordan, frames. We show that the conformal transformation between these two frames is not well defined in the extremal limit. We explore a set of definitions for surface gravity and observe the different predictions they make for the near extremal configuration of this black hole. Finally, motivated by the singularity structure in the interior of the event horizon in the Jordan frame, we use a holographic argument to remove the micro-states from the disconnected region of this solution. In this manner, we obtain a temperature which agrees with the standard results in the non-extremal regime, and which has a desirable behaviour around the extremal configurations.
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http://arxiv.org/abs/1209.4058
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