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Phases of Five-Dimensional Black Holes

We argue that the configurations that approach maximal entropy in five-dimensional asymptotically flat vacuum gravity, for fixed mass and angular momentum, are `black Saturns' with a central, close to static, black hole and a very thin black ring around it

a r X i v :h e p -t h /0702111v 3 24 A p r 2007hep-th/0702111

MIT-CTP-3812

Phases of Five-Dimensional Black Holes Henriette Elvang a ,Roberto Emparan b,c and Pau Figueras c a Center for Theoretical Physics Massachusetts Institute of Technology,Cambridge MA 02139,USA b Instituci´o Catalana de Recerca i Estudis Avan¸c ats (ICREA)c Departament de F´ısica Fonamental Universitat de Barcelona,Diagonal 647,E-08028Barcelona,Spain elvang@lns.mit.edu,emparan@ub.edu,pfigueras@ffn.ub.es

Abstract

We argue that the configurations that approach maximal entropy in five-dimen-sional asymptotically flat vacuum gravity,for fixed mass and angular momentum,are ‘black Saturns’with a central,close to static,black hole and a very thin black ring around it.For any value of the angular momentum,the upper bound on the entropy is equal to the entropy of a static black hole of the same total mass.For fixed mass,spin and area there are families of multi-ring solutions with an arbitrarily large number of continuous parameters,so the total phase space is infinite-dimensional.Somewhat surprisingly,the phases of highest entropy are not in thermal equilibrium.Imposing thermodynamical equilibrium drastically reduces the phase space to a finite,small number of different phases.

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