Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-12-07
Phys.Rev. D71 (2005) 044016; Erratum-ibid. D71 (2006) 029904
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
21 pages Latex file, 1 figure; discussion on integrability rectified, typo in (2.14) corrected
Scientific paper
10.1103/PhysRevD.71.044016
By using suitably improved surface integrals, we give a unified geometric derivation of the generalized Smarr relation for higher dimensional Kerr black holes which is valid both in flat and in anti-de Sitter backgrounds. The improvement of the surface integrals, which allows one to use them simultaneously at infinity and on the horizon, consists in integrating them along a path in solution space. Path independence of the improved charges is discussed and explicitly proved for the higher dimensional Kerr AdS black holes. It is also shown that the charges for these black holes can be correctly computed from the standard Hamiltonian or Lagrangian surface integrals.
Barnich Glenn
Compere Geoffrey
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