Advertisement

General Relativity and Gravitation

, Volume 38, Issue 8, pp 1305–1315 | Cite as

Flat Information Geometries in Black Hole Thermodynamics

  • Jan E. Åman
  • Ingemar Bengtsson
  • Narit Pidokrajt
Research Article

Abstract

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein–Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.

Keywords

Black Hole Event Horizon Black Ring Extremal Black Hole Kerr Black Hole 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hawking S.W.(1975). Particle creation by black holes. Commun. Math. Phys. 43, 199CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Weinhold F.(1976). Thermodynamics and geometry. Phys. Today March 23Google Scholar
  3. 3.
    Ruppeiner, G.: Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 67, 605 (1995); 68, 313(E) (1996)Google Scholar
  4. 4.
    Å man J.E., Bengtsson I., Pidokrajt N.(2003). Geometry of black hole thermodynamics. Gen. Rel. Grav. 35: 1733CrossRefADSGoogle Scholar
  5. 5.
    Å man J.E., Pidokrajt N.(2006). Geometry of higher-dimensional black hole thermodynamics. Phys. Rev. D 73: 024017CrossRefADSMathSciNetGoogle Scholar
  6. 6.
    Johnston D.A., Janke W., Kenna R.(2003). Information geometry, one, two, three (and four). Acta Phys. Polon. B 34: 4923ADSMathSciNetMATHGoogle Scholar
  7. 7.
    Arcioni G., Lozano-Tellechea E.(2005). Stability and critical phenomena of black holes and black rings. Phys. Rev. D 72: 104021CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Ferrara S., Gibbons G.W., Kallosh R.(1997). Black holes and critical points in moduli space. Nucl. Phys. B 500: 75CrossRefADSMathSciNetMATHGoogle Scholar
  9. 9.
    Shen, J., Cai, R.G., Wang, B., Su, R.K.: Thermodynamic geometry and critical behaviour of black holes. arXiv preprint gr-gc/0512035Google Scholar
  10. 10.
    Bengtsson I., Życzkowski K.(2006). Geometry of Quantum States. Cambridge University Press, CambridgeMATHGoogle Scholar
  11. 11.
    Hankey A., Stanley H.E.(1972). Systematic application of generalized homogeneous functions to static scaling, dynamic scaling, and universality. Phys. Rev. B 6: 3515CrossRefADSGoogle Scholar
  12. 12.
    Dubrovin B.: Geometry of 2D topological field theories. In: Francaviglia, M., Greco, S.(eds) Integrable Systems and Quantum Groups. Lecture Notes in Mathematics, vol. 1620. Berlin (1996)Google Scholar
  13. 13.
    Emparan R., Reall H.S.(2002). A rotating black ring in five dimensions. Phys. Rev. Lett. 88: 101101CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    Myers R.C., Perry M.J.(1986). Black holes in higherdimensional space-times. Ann. Phys. 172: 304CrossRefADSMathSciNetMATHGoogle Scholar
  15. 15.
    Bañados M., Teitelboim C., Zanelli J.(1992). The black hole in three-dimensional spacetime. Phys. Rev. Lett. 69: 1849CrossRefADSMathSciNetMATHGoogle Scholar
  16. 16.
    Nulton J.D., Salamon P.(1985). Geometry of the ideal gas. Phys. Rev. A 31: 2520CrossRefADSGoogle Scholar
  17. 17.
    Davies P.C.W.(1977). The thermodynamic theory of black holes. Proc. Roy. Soc. A 353: 499CrossRefADSGoogle Scholar
  18. 18.
    Tranah D., Landsberg P.T.(1980). Thermodynamics of non-extensive entropies II. Collect Phenom. 3: 73MathSciNetGoogle Scholar
  19. 19.
    Penrose R.(2004). The Road to Reality. Jonathan Cape, LondonGoogle Scholar
  20. 20.
    Sorkin R.(1982). A stability criterion for many-parameter families. Astrophys. J. 257: 847CrossRefADSMathSciNetGoogle Scholar
  21. 21.
    Katz J., Okamoto I., Kaburaki O.(1993). Thermodynamic stability of pure black holes. Class. Quant. Grav. 10: 1323CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    Lynden-Bell D.(1998). Negative specific heat in astronomy, physics and chemistry. In: Proceeding of XXth IUPAP Conference on Statistical Physics. Kluwer, DordrechtGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Jan E. Åman
    • 1
  • Ingemar Bengtsson
    • 1
  • Narit Pidokrajt
    • 1
  1. 1.AlbaNova FysikumStockholm UniversityStockholmSweden

Personalised recommendations