Horizon multipole moments of a Kerr black hole are computed in closed form from two definitions, yielding different values for l >= 1 at nonzero spin and sharing parity and small-spin scaling with field multipoles.
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Quasi-local dynamical horizons admit a first law for finite, far-from-equilibrium processes and a quantitative second law tying area growth to energy fluxes, so black-hole entropy is the area of marginally trapped surfaces.
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Horizon Multipole Moments of a Kerr Black Hole
Horizon multipole moments of a Kerr black hole are computed in closed form from two definitions, yielding different values for l >= 1 at nonzero spin and sharing parity and small-spin scaling with field multipoles.
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Thermodynamics of dynamical black holes beyond perturbation theory
Quasi-local dynamical horizons admit a first law for finite, far-from-equilibrium processes and a quantitative second law tying area growth to energy fluxes, so black-hole entropy is the area of marginally trapped surfaces.