Even the most extreme objects in the universe – including black holes – must obey certain rules.
A central law for black holes predicts that the total area of their event horizons – the boundary beyond which nothing can ever escape – should never shrink. This law is Hawking’s area theorem, named after physicist Stephen Hawking, who derived the theorem in 1971.
Fifty years later, physicists at Cornell, MIT and elsewhere have confirmed Hawking's area theorem for the first time, using observations of gravitational waves. Their results appeared in Physical Review Letters on July 1.
In the study, the researchers take a closer look at GW150914, the first gravitational wave signal detected by the Laser Interferometer Gravitational-wave Observatory (LIGO), in 2015, which was confirmed using a theoretical model developed at Cornell. The signal was a product of two inspiraling black holes that merged to produce a new black hole, along with a huge amount of energy that rippled across space-time as gravitational waves.
“The idea that you could actually test Hawking’s Area Theorem seems crazy,” said Saul Teukolsky, the Hans Bethe Professor of Physics in the College of Arts and Sciences and a co-author of the paper. “You have to go out somewhere and find some black holes, measure their areas and add them up, then come back later when they’ve merged and measure the area of the final black hole. Luckily, this is something we can do by analyzing the gravitational waves the system emits.”
If Hawking's area theorem holds, then the horizon area of the new black hole should not be smaller than the total horizon area of its parent black holes. In the new study, the physicists reanalyzed the signal from GW150914 before and after the cosmic collision and found that indeed, the total event horizon area did not decrease after the merger -- a result that they report with 95 percent confidence.
Their findings mark the first direct observational confirmation of Hawking's area theorem, which has been proven mathematically but never observed in nature until now. The team plans to test future gravitational-wave signals to see if they might further confirm Hawking's theorem or be a sign of new, law-bending physics.
In 1971, Stephen Hawking proposed the area theorem, which set off a series of fundamental insights about black hole mechanics. The statement was a curious parallel of the second law of thermodynamics, which states that the entropy, or degree of disorder within an object, should also never decrease.
The similarity between the two theories suggested that black holes could behave as thermal, heat-emitting objects -- a confounding proposition, as black holes by their very nature were thought to never let energy escape, or radiate. Hawking eventually squared the two ideas in 1974, showing that black holes could have entropy and emit radiation over very long timescales if their quantum effects were taken into account. This phenomenon was dubbed "Hawking radiation" and remains one of the most fundamental revelations about black holes.
"It all started with Hawking's realization that the total horizon area in black holes can never go down. The area law encapsulates a golden age in the '70s where all these insights were being produced," said lead author Maximiliano Isi, a NASA Einstein Postdoctoral Fellow at MIT.
Hawking and others have since shown that the area theorem works out mathematically, but there had been no way to check it against nature until LIGO's first detection of gravitational waves.
In 2019, Matthew Giesler, research associate at the Cornell Center for Astrophysics and Planetary Science (A&S), and the new paper's other co-authors developed a technique to extract the reverberations immediately following GW150914's peak -- the moment when the two parent black holes collided to form a new black hole. The team used the technique to pick out specific frequencies, or tones of the otherwise noisy aftermath, that they could use to calculate the final black hole's mass and spin.
They then developed a model to analyze the signal before the peak, corresponding to the two inspiraling black holes, and to identify the mass and spin of both black holes before they merged. From these estimates, they calculated their total horizon areas -- an estimate roughly equal to about 235,000 square kilometers, or roughly twice the area of New York State.
They used their previous technique to extract the "ringdown," or reverberations of the newly formed black hole, from which they calculated its mass and spin, and ultimately its horizon area, which they found was equivalent to 367,000 square kilometers (approximately three times the area of New York).
"The data show with overwhelming confidence that the horizon area increased after the merger, and that the area law is satisfied with very high probability," Isi said. "It was a relief that our result does agree with the paradigm that we expect, and does confirm our understanding of these complicated black hole mergers."
The team plans to further test Hawking's area theorem, and other longstanding theories of black hole mechanics, using data from LIGO and Virgo, its counterpart in Italy.
“It’s exciting that the novel methods we developed to reanalyze the first merger have now allowed us to finally put Hawking’s proposition to the test,” said Giesler. “The area theorem is really a statement about Einstein’s theory of relativity, so we’re putting Einstein to the test here. As detectors improve, we’ll continue to probe the gravitational waves from black holes with exceptional precision, constantly looking for the point where Einstein’s theory might finally break down.”
Other co-authors on the paper are Will Farr of Stony Brook University and the Flatiron Institute's Center for Computational Astrophysics and Mark Scheel of Caltech.
The research was supported, in part, by NASA, the Simons Foundation, and the National Science Foundation.
A version of this story also appears in the Cornell Chronicle.
