Derives a Christodoulou-Ruffini-type squared-mass formula for Kerr-Newman-NUT-AdS4 using secondary NUT hairs J_n and N, then verifies the first law and Smarr relation by differentiation.
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Generalized Bardeen black holes show two topological defects of opposite winding numbers yielding zero total charge in their thermodynamic vector field, unlike Schwarzschild's single unstable branch, with regularization parameters shaping the phase structure.
Topological numbers categorize black hole systems into universality classes based on thermodynamic behavior, with calculations for critical points and phase transitions.
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