Geometry and topology of two kinds of extreme Reissner-Nordström-anti-de Sitter black holes

Abstract

Different geometrical and topological properties have been shown for two kinds of extreme Reissner-Nordström-anti-de Sitter black holes. The relationship between the geometrical properties and the intrinsic thermodynamical properties has been made explicit. PACS number(s): 04.70.Dy, 04.20.Gz, 04.62.+v. e-mail:binwang@fma.if.usp.br e-mail:eabdalla@fma.if.usp.br e-mail:rksu@fudan.ac.cn 1 The study of the extreme black hole (EBH) has been stimulated since the discovery [1,2] that the four-dimensional (4D) Reissner-Nordström (RN) EBH is a different object from its nonextreme counterpart owing to its drastically different topological properties and peculiar zero entropy regardless of its nonzero horizon area. However, these results met some challenges subsequently. Starting with the grand canonical ensemble, it was argued [3-5] that in a finite size cavity a 4D RN non-extreme black hole (NEBH) can approach the extreme state as closely as one likes and the geometrical and topological properies are still of nonextreme sectors. Bekenstein-Hawking formula is believed to hold for RN EBH entropy description, which is also supported by state-counting calculations of certain extreme and near-extreme black holes in string theory, see [6] for a review. These different results indicate that EBHs have a controversial role in black hole thermodynamics and topologies and require special care. Comparing [1,2] and [3-5], it seems that the clash comes from two different treatments: one refers to Hawking’s treatment by starting with the original EBH [1,2] and the other Zaslavskii’s treatment by first taking the boundary limit and then the extreme limit to get the EBH from its nonextreme counterpart [3-5]. Applying these two treatments, it was found that two different topological objects represented by different Euler characteristics exist for 4D RN EBH, charged dilaton EBH [7], Kerr EBH [8] as well as two-dimensional (2D) EBHs [7,9]. Drastically different intrinsic thermodynamical properties have also been displayed for 4D Kerr EBH [8] and 2D EBHs [9,10] due to these different treatments. Based upon these results it was suggested that there maybe two kinds of EBHs in nature: the first kind suggested by Hawking et al with the extreme topology and zero entropy, which can only be formed by pair

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Cite this paper

@inproceedings{Wang1999GeometryAT, title={Geometry and topology of two kinds of extreme Reissner-Nordström-anti-de Sitter black holes}, author={Bin Wang and Elcio Abdalla}, year={1999} }