Over a century after Einstein published his theory of general relativity, researchers at the University of Cambridge have upended one of the most fundamental rules governing black holes—the so-called 3rd law of black hole mechanics. Their findings, published in Physical Review Letters, suggest that extremal black holes, those spinning or charged to their absolute theoretical limit, can form in finite time in vacuum gravity, a result that fundamentally challenges decades of accepted physics.
For nearly half a century, the 3rd law of black hole mechanics has been treated as settled science. Formulated by Bardeen, Carter, and Hawking in 1973 and seemingly proven by physicist Werner Israel in 1986, the law stated that it should be impossible to reduce a black hole's temperature to absolute zero—to create what physicists call an "extremal" black hole—in any realistic scenario. Extremal black holes are peculiar objects: they would have zero surface gravity and emit no Hawking radiation, making them thermodynamically frozen in time.
The crack in this seemingly ironclad rule first appeared in 2022, when Ryan Unger and Christoph Kehle discovered a fatal flaw in Israel's proof. They demonstrated that the 3rd law could indeed be violated—at least for electrically charged black holes that absorb idealized charged matter. "This was huge news," said John R. Crump, first author of the Cambridge team's paper, "and the natural question on everyone's minds was 'if the 3rd law is false for charged black holes, what about for black holes without any matter at all?'"
The Cambridge team's answer came through numerical simulations that took the investigation further: they demonstrated that an extremal rotating black hole could form from a pre-existing Schwarzschild black hole—a non-rotating black hole with mass but no electric charge—in a vacuum, with no matter, gas, or radiation present. The mechanism they explored was elegantly simple: gravitational waves alone could carry away enough energy for a black hole to reach zero temperature in finite time.
Working in five dimensions rather than our familiar four, the researchers employed a mathematical technique called characteristic gluing. As Crump explained, this approach allows physicists to "glue" together different regions of spacetime into a larger spacetime that satisfies Einstein's equations. In this case, they connected an initial region containing an ordinary Schwarzschild black hole to a final region containing an extremal Myers-Perry black hole—the five-dimensional cousin of a rotating extremal black hole.
The choice to work in five dimensions was pragmatic rather than science fiction. "Surprisingly, it's considerably easier to set up the problem in 5d because there is a symmetry that can be exploited, and this symmetry isn't there in 4d," Crump noted. Yet he emphasized that even this abstract result matters: "Showing this result for vacuum gravity in 5d is still a coup that enriches our understanding of general relativity—after 111 years it feels as though Einstein's theory of gravity usually only becomes more mysterious rather than less."
The implications ripple outward. Black holes have long been understood through the lens of thermodynamics, obeying laws that parallel the laws governing heat and entropy. Crump reflected on the philosophical shift: "One of the most profound insights in the history of black holes was Jacob Bekenstein's proposal that they are thermodynamic objects." Now, physicists must reconsider which of these thermodynamic principles truly hold universal sway. The discovery opens new questions about the fundamental nature of spacetime and whether other accepted laws of black hole mechanics might yet be overthrown.