A pot of boiling water is covered with two lids — an inner and an outer one. The thermometer under each shows its own temperature, but their harmonic mean (a special averaging method where you add the reciprocals) always remains unchanged. Heat seems to obey an invisible rule. The thermodynamics of black holes with a NUT charge, a peculiar gravitational parameter reminiscent of a magnetic charge, works in a similar way.
The physicists decided to test whether such a hole can be described honestly — not by tweaking temperatures to fit the answer, but by measuring them at both horizons. It turned out that a complete picture requires accounting for hidden rotation. This quantity is not like the familiar rotation of a star; it arises from a combination of mass and NUT charge, as if an invisible flywheel spins deep inside the hole.
This approach is reminiscent of diagnosing an engine by sound: without looking under the hood, you can detect a hidden malfunction. Here, the "sound" is played by thermal relations, and the "engine" is the black hole itself.
The NUT charge is named after three scientists (Newman, Unti, and Tamburino) and behaves almost like a magnetic monopole, but in gravity.
In Greg Egan's novel "The Light of Other Days," travelers encounter black holes whose hidden parameters alter the laws of physics around them.