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Geometry of black hole thermodynamics
Stockholm University, Faculty of Science, Department of Physics. (Quantum and Field Theory)
Stockholm University, Faculty of Science, Department of Physics. (Quantum and Field Theory)
Stockholm University, Faculty of Science, Department of Physics. (Quantum and Field Theory)
2003 (English)In: General Relativity and Gravitation, ISSN 0001-7701, Vol. 35, no 10, 1733-1743 p.Article in journal (Refereed) Published
Abstract [en]

The Hessian of the entropy function can be thought of as a metric tensor on the state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study this geometry for some families of black holes. It is flat for the BTZ and Reissner-Nordstrom black holes, while curvature singularities occur for the Reissner-Nordstrom-anti-de Sitter and Kerr black holes.

Place, publisher, year, edition, pages
Germany: Springer , 2003. Vol. 35, no 10, 1733-1743 p.
Keyword [en]
black hole, entropy, hessian
National Category
Other Physics Topics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-29359DOI: 10.1023/A:1026058111582OAI: oai:DiVA.org:su-29359DiVA: diva2:232729
Projects
Geometry and Physics
Available from: 2009-08-25 Created: 2009-08-25 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.
Keyword
black holes, thermodynamics, instability, hessian, entropy, ruppeiner geometry, weinhold geometry, information geometry
National Category
Other Physics Topics
Research subject
Theoretical Physics
Identifiers
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)
Opponent
Supervisors
Projects
Geometry and Physics
Note
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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