Adapting Barnich-Compère conserved charges, the first law requires unvarying components for both the Killing vector and AdS background (true for E's ξ but not F's β), while V_C enters the β-Smarr relation due to simplifications from the principal conformal Killing-Yano tensor.
Generalized Smarr relation for Kerr AdS black holes from improved surface integrals
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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 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.
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gr-qc 1years
2026 1verdicts
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The Role of the Volume in Black Hole Thermodynamics
Adapting Barnich-Compère conserved charges, the first law requires unvarying components for both the Killing vector and AdS background (true for E's ξ but not F's β), while V_C enters the β-Smarr relation due to simplifications from the principal conformal Killing-Yano tensor.