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

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. ∗ Senior Research Associate of the National Fund for Scientific Research (Belgium). E-mail: [email protected] † Research Fellow of the National Fund for Scientific Research (Belgium). E-mail: [email protected] Geometric derivation of Smarr relation for Kerr AdS BH 2