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Generalized Smarr relation for Kerr-AdS black holes from improved surface integrals

Glenn Barnich* and Geoffrey Compère†

  • Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles, Belgium

  • *Electronic address: gbarnich@ulb.ac.be
  • †Electronic address: gcompere@ulb.ac.be
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Phys. Rev. D 71, 044016 – Published 11 February, 2005Erratum Phys. Rev. D 73, 029904 (2006)

DOI: https://doi.org/10.1103/PhysRevD.71.044016

Abstract

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 explicitly proved. It is also shown that the charges for higher dimensional Kerr-AdS black holes can be correctly computed from the standard Hamiltonian or Lagrangian surface integrals.

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Erratum

Erratum: Generalized Smarr relation for Kerr-AdS black holes from improved surface integrals [Phys. Rev. D 71, 044016 (2005)]

Glenn Barnich and Geoffrey Compère
Phys. Rev. D 73, 029904 (2006)

Article Text

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Phys. Rev. D 71, 044016– Published 11 February, 2005
  • Received 4 January 2005

© 2005 American Physical Society

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