A note on conserved charges of asymptotically flat and anti-de Sitter spaces in arbitrary dimensions |
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Authors: | Ella Jamsin |
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Institution: | (1) Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, 1050 Bruxelles, Belgium |
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Abstract: | The calculation of conserved charges of black holes is a rich problem, for which many methods are known. Until recently, there
was some controversy on the proper definition of conserved charges in asymptotically anti-de Sitter (AdS) spaces in arbitrary
dimensions. This paper provides a systematic and explicit Hamiltonian derivation of the energy and the angular momenta of
both asymptotically flat and asymptotically AdS spacetimes in any dimension D ≥ 4. This requires as a first step a precise determination of the asymptotic conditions of the metric and of its conjugate
momentum. These conditions happen to be achieved in ellipsoidal coordinates adapted to the rotating solutions. The asymptotic
symmetry algebra is found to be isomorphic either to the Poincaré algebra or to the so(D − 1,2) algebra, as expected. In the asymptotically flat case, the boundary conditions involve a generalization of the parity
conditions, introduced by Regge and Teitelboim, which are necessary to make the angular momenta finite. The charges are explicitly
computed for Kerr and Kerr–AdS black holes for arbitrary D and they are shown to be in agreement with thermodynamical arguments.
The author is a FRIA-FNRS bursar (National Fund for Scientific Research, Belgium). |
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Keywords: | Conserved charges Hamiltonian formulation of general relativity Higher dimensions |
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