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Geometry of higher-dimensional black hole thermodynamics
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
2006 (English)In: Physical Review D. Particles and fields, ISSN 0556-2821, Vol. 73, no 2, 024017- p.Article in journal (Refereed) Published
Abstract [en]

We investigate thermodynamic curvatures of the Kerr and Reissner-Nordström (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a d=5 Kerr black hole is curved and divergent in the extremal limit. For a d>=6 Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In d>=5 the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in d=5 with double angular momenta.

Place, publisher, year, edition, pages
2006. Vol. 73, no 2, 024017- p.
URN: urn:nbn:se:su:diva-12519DOI: 10.1103/PhysRevD.73.024017OAI: diva2:179039
Available from: 2008-01-15 Created: 2008-01-15 Last updated: 2009-08-25Bibliographically approved
In thesis
1. Information geometries in black hole physics
Open this publication in new window or tab >>Information geometries in black hole physics
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we aim to develop new perspectives on the statistical mechanics of black holes using an information geometric approach (Ruppeiner and Weinhold geometry). The Ruppeiner metric is defined as a Hessian matrix on a Gibbs surface, and provides a geometric description of thermodynamic systems in equilibrium. This Ruppeiner geometry exhibits physically suggestive features; a flat Ruppeiner metric for systems with no interactions i.e. the ideal gas, and curvature singularities signaling critical behavior(s) of the system. We construct a flatness theorem based on the scaling property of the black holes, which proves to be useful in many cases. Another thermodynamic geometry known as the Weinhold geometry is defined as the Hessian of internal energy and is conformally related to the Ruppeiner metric with the system’s temperature as a conformal factor.

 We investigate a number of black hole families in various gravity theories. Our findings are briefly summarized as follows: the Reissner-Nordström type, the Einstein-Maxwell-dilaton andBTZ black holes have flat Ruppeiner metrics that can be represented by a unique state space diagram. We conjecture that the state space diagram encodes extremality properties of the black hole solution. The Kerr type black holes have curved Ruppeiner metrics whose curvature singularities are meaningful in five dimensions and higher, signifying the onset of thermodynamic instabilities of the black hole in higher dimensions. All the three-parameter black hole families in our study have non-flat Ruppeiner and Weinhold metrics and their associated curvature singularities occur in the extremal limits. We also study two-dimensional black hole families whose thermodynamic geometries are dependent on parameters that determine the thermodynamics of the black hole in question. The tidal charged black hole which arises in the braneworld gravity is studied. Despite its similarity to the Reissner-Nordström type, its thermodynamic geometries are distinctive.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2009. xiv + 89 p.
black holes, thermodynamics, instability, hessian, entropy, ruppeiner geometry, weinhold geometry, information geometry
National Category
Other Physics Topics
Research subject
Theoretical Physics
urn:nbn:se:su:diva-29365 (URN)978-91-7155-916-6 (ISBN)
Public defence
2009-09-21, sal FD41, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Geometry and Physics
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Submitted. Available from: 2009-08-30 Created: 2009-08-25 Last updated: 2009-08-25Bibliographically approved

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Åman, Jan E.Pidokrajt, Narit
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