Gas passing through a narrow valve can heat up or cool down: this is the Joule–Thomson effect, which powers refrigerators and air liquefiers. It turns out black holes can do the same. The authors considered a charged black hole in anti-de Sitter space (a world with constant negative curvature, like a saddle), adding corrections from modified gravity and nonlinear electrodynamics (where fields are so strong that Maxwell's laws stop being linear).

The main takeaway: the black hole's charge black hole is the most powerful regulator of its thermal behavior. By changing the charge, you can make the hole cool or heat at the same pressure. Additional parameters, modified gravity and the nonlinear electromagnetic field, only slightly adjust the picture, like fine-tuning knobs. At distances comparable to interstellar scales, the geometry of spacetime curved spacetime is almost indistinguishable from the predictions of standard theory, allowing the model to be applied to real astrophysical objects.

So a black hole becomes like a heat engine with a main regulator — electric charge. Change the charge, and you switch the mode from heating to cooling. This same charge brings us back to the familiar picture of distant space: at large distances, the hole looks like an ordinary massive object, and only up close do the quirks of modified gravity show up.