What counts as a black hole's hidden properties in curved spacetime?

Black holes in anti-de Sitter spacetime with NUT charge—a topological parameter—behave like they have two extra thermodynamic properties beyond mass, charge, and spin. Researchers showed these "secondary hairs" are not new metric parameters but emerge naturally when you define the thermodynamic state correctly, allowing them to write down all the black hole's properties (temperature, entropy, potential) from a single equation. This settles an ambiguity in how to measure spacetime volume for these exotic black holes.