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Thermodynamics of tidal charged black holes
Stockholm University, Faculty of Science, Department of Physics. (Quantum and Field Theory)
Szeged University, Hungary.
Munich University, Germany.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We study the thermodynamics of tidal charged black holes in four dimensions. Such black holes are spherically symmetric vacuum solutions of the effective Einstein equations on the brane and are characterized by the mass m and (generalizing their general relativistic counterparts) by a second parameter, the tidal charge q. The latter is an imprint of the Weyl curvature of the 5-dimensional space-time, in which the brane is embedded. The heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space. However, there is no phase transition at those points, similarly to the Reissner-Nordstr\"om black hole. We investigate the thermodynamic geometry of such black holes by deriving the Weinhold and the Ruppeiner metrics. Whereas the Weinhold metric is flat, the Ruppeiner metric has a positive Ricci curvature, which is in sharp contrast with the Reissner-Nordstr\"om black hole, the general relativistic analogue of the tidal charged metric. The state space is conformal to the right half of the interior of the future light cone in a Minkowski plane. We find two constraints on the possible 5-dimensional extensions of the tidal-charged black hole: First, we conjecture that the 5-dimensional black object should have the same entropy as its 4-dimensional section studied here, modulo corrections which are small for large black holes. Second, for constant m any quasi-stationary evolution of the tidal charged black hole leads to a decrease of q, contributing towards the localization of gravity on the brane. This represents an important constraint on the evolution of the 5-dimensional space-time.

Keyword [en]
black holes, thermodynamics, tidal charged, braneworld
National Category
Other Physics Topics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-29361OAI: oai:DiVA.org:su-29361DiVA: diva2:232733
Available from: 2009-08-25 Created: 2009-08-25 Last updated: 2010-01-14Bibliographically 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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