Physicists Rewrite Hawking's Black Hole Laws to Work on Real, Ever-Changing Black Holes

For half a century, the laws that link black holes to the rules of heat and entropy came with an asterisk: they only truly applied to black holes that were perfectly still and unchanging. Now physicists at Penn State say they have found a way to extend those laws to the messy, dynamic black holes that actually populate the universe — the ones that form, swallow matter, collide and slowly evaporate.

The original framework, built on the work of Stephen Hawking and others in the 1970s, drew a beautiful parallel between the mechanics of black holes and the four laws of thermodynamics, treating the area of a black hole's event horizon as a stand-in for its entropy. "They were formulated for black holes at equilibrium, or unchanging over time, but black holes are constantly changing," said Abhay Ashtekar, the Penn State physicist who led the new work.

Ashtekar and graduate students Daniel E. Paraizo and Jonathan Shu argue that the event horizon — defined by the black hole's entire future history — is the wrong yardstick for an object in flux. "The area of event horizons cannot be a measure of the physical entropy of dynamical black holes," Shu said. In its place, the team introduces a new entropy measure tied to a "dynamical horizon," defined by the black hole's properties at a given moment rather than by predictions about what it will do in the future.

The reframing, published in Physical Review Letters and selected as an Editor's Suggestion, opens the door to applying the powerful tools of thermodynamics — concepts like entropy and temperature — to non-equilibrium black holes for the first time in a rigorous way. "This opened the door to finding analogies in black holes of entropy and temperature used in thermodynamics," Paraizo said.

The payoff could be practical as well as conceptual. A thermodynamics that works on changing black holes should give physicists a sharper handle on the violent mergers and evaporations that dominate the real cosmos, including the black hole collisions detected as ripples in spacetime by the LIGO-Virgo-KAGRA gravitational-wave observatories. As detectors grow more sensitive and catch ever more of these events, having a theory that describes black holes as they truly are — restless, growing and shrinking — rather than as frozen idealizations could help decode what the universe's most extreme objects are really doing. The team's approach reframes a black hole not as a fixed object defined by its ultimate fate, but as an evolving system that can be described moment to moment, much as a physicist would track a cooling cup of coffee. That shift could prove especially valuable as gravitational-wave detectors record more mergers each year, giving theorists a language precise enough to match the flood of new data about black holes caught in the act of changing.