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.
Conserved Charges and First Law of Thermodynamics for Kerr-de Sitter Black Holes
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abstract
Recently, a general method for calculating conserved charges for (black hole) solutions to generally covariant gravitational theories, in any dimensions and with arbitrary asymptotic behaviors has been introduced. Equipped with this method, which can be dubbed as "solution phase space method," we calculate mass and angular momentum for the Kerr-dS black holes. Furthermore, for any choice of horizons, associated entropy and the first law of thermodynamics are derived. Interestingly, according to insensitivity of the analysis to the chosen cosmological constant, the analysis unifies the thermodynamics of rotating stationary black holes in 4 (and other) dimensions with either AdS, flat or dS asymptotics. We extend the analysis to include electric charge, i.e. to the Kerr-Newman-dS black holes.
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gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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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.