Geometry of higherdimensional black hole thermodynamics
Abstract
We investigate thermodynamic curvatures of the Kerr and ReissnerNordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in fourdimensional 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.
 Authors:
 Quantum and Field Theory group, Department of Physics, AlbaNova, Stockholm University, SE106 91 Stockholm (Sweden)
 Publication Date:
 OSTI Identifier:
 20795734
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.73.024017; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANGULAR MOMENTUM; BLACK HOLES; CONFIGURATION; COSMOLOGY; GEOMETRY; MANYDIMENSIONAL CALCULATIONS; SPACETIME; THERMODYNAMICS
Citation Formats
Aaman, Jan E., and Pidokrajt, Narit. Geometry of higherdimensional black hole thermodynamics. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.0.
Aaman, Jan E., & Pidokrajt, Narit. Geometry of higherdimensional black hole thermodynamics. United States. doi:10.1103/PHYSREVD.73.0.
Aaman, Jan E., and Pidokrajt, Narit. Sun .
"Geometry of higherdimensional black hole thermodynamics". United States.
doi:10.1103/PHYSREVD.73.0.
@article{osti_20795734,
title = {Geometry of higherdimensional black hole thermodynamics},
author = {Aaman, Jan E. and Pidokrajt, Narit},
abstractNote = {We investigate thermodynamic curvatures of the Kerr and ReissnerNordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in fourdimensional 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.},
doi = {10.1103/PHYSREVD.73.0},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 73,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}

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