Black hole entropy in diffeomorphism-invariant nonminimal gravity decomposes as S_H = S_W + S_1 + ΔS, with the extra terms required for bumblebee and Weyl-vector Gauss-Bonnet solutions but not for regular Kalb-Ramond branches.
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The Smarr formula is structurally identical to the single-copy Gauss's law for Kerr-Schild black holes, with the AdS pressure-volume term arising from gauge background subtraction.
GW250114 data confirm the remnant is consistent with a Kerr black hole and bound the dominant quadrupolar mode frequency to within a few percent of the GR prediction, with constraints tighter than prior multi-event catalogs.
Multi-fractional Schwarzschild black holes have profile-insensitive Noether mass and geometric area-law entropy, but require an extended first law with work terms for the q-profile parameters to restore integrability of the Clausius relation.
Deformation parameters α, β, σ in a quintessence AdS black hole shift the temperature minimum, enlarge the cooling region, raise inversion temperature, and alter heat-engine efficiency.
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The Smarr Formula is Gauss's Law: A Kerr-Schild Single-Copy Perspective
The Smarr formula is structurally identical to the single-copy Gauss's law for Kerr-Schild black holes, with the AdS pressure-volume term arising from gauge background subtraction.
- Supersymmetry and Attractors in N = 4 Supergravity: The Superconformal Approach