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Introduction to Anti de Sitter Black Holes

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From Gravity to Thermal Gauge Theories: The AdS/CFT Correspondence

Part of the book series: Lecture Notes in Physics ((LNP,volume 828))

Abstract

These introductory notes concern basic properties of negative constant curvature spacetimes and their black holes. For comparison purposes we will begin by reviewing flat spacetime, the spacetime diagram and two particular patches, Milne and Rindler. We will then discuss anti de Sitter, its symmetries, basic properties and the construction of the spacetime diagram. We then look into the properties of anti de Sitter spacetime giving some global and local parametrisations. We will study the static black holes and then discuss their basic properties and novel topological effects due to the presence of a negative cosmological constant. We show using the classical Euclidean path integral approach their thermodynamic properties in the canonical ensemble with a heat bath of constant temperature. Finally we discuss, rather briefly, stationary and axially symmetric spacetimes and some properties of the rotating black holes.

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Notes

  1. 1.

    The boundary is called conformal for it admits not one but an equivalence class of metrics which are related via a conformal transformation, \(g_{\mu\nu}^{boundary}=\Upomega \Upgamma_{\mu\nu}^{boundary}.\) This equivalence class is manifest in the arbitrariness of \(\Uplambda\) in (1.16).

  2. 2.

    This is quite unlike the situation for Kerr’s solution at asymptotic infinity.

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Acknowledgements

It is a pleasure to thank Bruno Boisseau, Jeff Dufaux, Renaud Parentani and Kostas Skenderis for helpful comments and discussion. I am especially grateful to Roberto Emparan and Bernard Linet for reading through the manuscript and making numerous helpful and critical comments and corrections. I last but not least thank Jihad Mourad for discussion and explanations regarding properties of adS space.

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Authors and Affiliations

  1. LPT, Université de Paris-Sud, Bât 210, 91405, Orsay CEDEX, France

    Christos Charmousis

  2. LMPT, Parc de Grandmont, Université Francois Rabelais, Tours, France

    Christos Charmousis

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  1. Christos Charmousis
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Correspondence to Christos Charmousis .

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Editors and Affiliations

  1. Dept.Physics, National Technical University, Zografou Campus, Athens, 157 80, Greece

    Eleftherios Papantonopoulos

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Charmousis, C. (2011). Introduction to Anti de Sitter Black Holes. In: Papantonopoulos, E. (eds) From Gravity to Thermal Gauge Theories: The AdS/CFT Correspondence. Lecture Notes in Physics, vol 828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04864-7_1

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  • DOI: https://doi.org/10.1007/978-3-642-04864-7_1

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