Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Homology

  • Ioannis P. Zois
Conference paper
Part of the Astrophysics and Space Science Library book series (ASSL, volume 276)

Abstract

We shall try to exhibit a relation between black hole entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces.

Keywords

Godbillon-Vey class String Theory Foliations Dynamical Systems Black Holes Topological Entropy 
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References

  1. [1]
    Zois, I.P.: “A new invariant for σ models”, Comrnun. Math. Phys. Vol 209 No 3 (2000) pp757–789 (communicated by A. Connes).MathSciNetADSMATHGoogle Scholar
  2. [2]
    Zois, I.P.: “The Godbillon-Vey class, Invariants of Manifolds and Linearised M-Theory”, hep-th/0006169, Oxford preprint, (submitted to Commun. Math. Phys., Prof. A. Connes).Google Scholar
  3. [3]
    Zois, I.P.: “Black Hole Entropy, Topological Entropy and Noncommutative Geometry”, hep-th/0104004, Oxford preprint.Google Scholar
  4. [4]
    A. Candel and L. Conlon: “Foliations I”, Graduate Studies in Mathematics Vol 23, American Mathematical Society, Providence Rhode Island 2000.MATHGoogle Scholar
  5. [5]
    A. Connes: “Non-commutative Geometry”. Academic Press 1994. A. Connes: “Noncommutative Geometry Year2000”,qal0011193.Google Scholar
  6. [6]
    A. Connes, M.R. Douglas and A. Schwarz: “Noncommutative Geometry and M-Theory: compactification on tori”, JHEP02, 003 (1998).Google Scholar
  7. [7]
    P. Baum and R. Douglas: “K-Homology and Index Theory”, Proc. Sympos. Pure Math. 38, Providence, Rhode Island AMS 1982.Google Scholar
  8. [8]
    E. Ghys, R. Langevin and P. Walczak: “Entropie geometrique des feuilletages”, Acta Math. 160(1995), 105–142.MathSciNetCrossRefGoogle Scholar
  9. [9]
    A. Strominger, C. Vafa: “Microscopic Origin of the Beckenstein-Hawking Entropy”, Phys. Lett. B379 (1996) 99–104. G. Horowitz, A. Strominger: “Counting States of Near-Extremal Black Holes”, Phys. Rev. Lett. 77 (1996) 2368-2371. G. Horowitz, J. Maldacena, A. Strominger: “Nonextremal Black Hole Microstates and U-duality”, Phys. Lett. B383 (1996) 151-159. G.T. Horowitz: “The Origin of Black Hole Entropy in String Theory”, Proceedings of the Pacific Conference on Gravitation and Cosmology, Seoul, Korea, February 1-6, 1996.MathSciNetGoogle Scholar
  10. [10]
    A. Konechny and A. Schwarz: “Moduli spaces of maximally supersymmetric solutions on noncommutative tori and noncommutative orbifolds”, JHEP 0009 (2000) 005. A. Konechny and A. Schwarz: “Compactification of M-Theory on noncommutative toroidal orbifolds”, Nucl. Phys. B591 (2000) 667-684. A. Konechny and A. Schwarz: “1/4-BPS states on noncommutative tori”,JHEP 9909 (1999) 030. A. Konechny and A. Schwarz: “Supersymmetry algebra and BPS states of super Yang-Mills theories on noncommutative tori”, Phys. Lett. B453 (1999) 23-29.Google Scholar
  11. [11]
    P.K. Townsend: “BlackHoles”, Lecture Notes, DAMTP Cambridge University, 1998.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Ioannis P. Zois
    • 1
  1. 1.Mathematical InstituteOxford UniversityOxford

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