There are certain rules that even the most extreme objects in the universe must obey. A central law for black holes predicts that the 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 MIT and elsewhere have now confirmed Hawking’s area theorem for the first time, using observations of gravitational waves. Their results appear today in
Physical Review Letters.
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. The signal was a product of two inspiraling black holes that generated a new black hole, along with a huge amount of energy that rippled across space-time as gravitational waves.
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.
“It is possible that there’s a zoo of different compact objects, and while some of them are the black holes that follow Einstein and Hawking’s laws, others may be slightly different beasts,” says lead author Maximiliano Isi, a NASA Einstein Postdoctoral Fellow in MIT’s Kavli Institute for Astrophysics and Space Research. “So, it’s not like you do this test once and it’s over. You do this once, and it’s the beginning.”
Isi’s co-authors on the paper are Will Farr of Stony Brook University and the Flatiron Institute’s Center for Computational Astrophysics, Matthew Giesler of Cornell University, Mark Scheel of Caltech, and Saul Teukolsky of Cornell University and Caltech.
In 1971, Stephen Hawking proposed the area theorem, which set off a series of fundamental insights about black hole mechanics. The theorem predicts that the total area of a black hole’s event horizon — and all black holes in the universe, for that matter — should never decrease. 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,” Isi says. “The area law encapsulates a golden age in the ’70s where all these insights were being produced.”
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.
Hawking, on hearing of the result, quickly contacted LIGO co-founder Kip Thorne, the Feynman Professor of Theoretical Physics at Caltech. His question: Could the detection confirm the area theorem?
At the time, researchers did not have the ability to pick out the necessary information within the signal, before and after the merger, to determine whether the final horizon area did not decrease, as Hawking’s theorem would assume. It wasn’t until several years later, and the development of a technique by Isi and his colleagues, when testing the area law became feasible.
In 2019, Isi and his colleagues 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.
A black hole’s mass and spin are directly related to the area of its event horizon, and Thorne, recalling Hawking’s query, approached them with a follow-up: Could they use the same technique to compare the signal before and after the merger, and confirm the area theorem?
The researchers took on the challenge, and again split the GW150914 signal at its peak. They 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 nine times the area of Massachusetts.
They then 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 13 times the Bay State’s area).
“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 says. “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 encouraging that we can think in new, creative ways about gravitational-wave data, and reach questions we thought we couldn’t before,” Isi says. “We can keep teasing out pieces of information that speak directly to the pillars of what we think we understand. One day, this data may reveal something we didn’t expect.”
This research was supported, in part, by NASA, the Simons Foundation, and the National Science Foundation.
See:
Hawking’s discovery started off with a simple-sounding question: Do black holes emit any heat? He had previously determined that black holes adhere to the second law of thermodynamics, which means that entropy (a measure of disorder) only increases over time. And as New Scientist
explains “anything that has entropy ... also has a temperature.”
In the 1970s, Hawking, using a lot of math, essentially took the temperature of a black hole.
He did this by combining insights from both Einstein’s theory of relativity (which describes how gravity works at grand scales) and quantum mechanics (which describes how the very smallest components of the universe work). These are the two major theories about how the universe works that scientists have been searching for decades to combine. And they both come into play at the event horizon of a black hole, the boundary beyond which gravity is so strong that not even light can escape.
Before Hawking’s discovery, black holes were typically thought to be objects into which things go in but never come out (the thinking actually stems in part from Hawking’s work describing singularities within black holes.)
Essentially, Hawking showed that black holes can, like so many objects in our universe, shrink and die. He even turned this insight into a bit of advice for us all: “Things can get out of a black hole. ... So if you feel you are in a black hole, don’t give up — there’s a way out.”
Here’s the explanation, and it’s pretty trippy.
Cliff Burgess, a physicist at McMaster University in Canada, walked me through it.
First off: Quantum mechanical theory explains that throughout the universe, particles and their counterparts, antiparticles, are constantly popping in and out of existence. Normally, when they pop into existence, they don’t last very long because a particle and its counterpart will quickly annihilate each other. (Thankfully, at the beginning of time, more matter was created than antimatter. Without that imbalance, the universe would have quickly destroyed itself.)
But life at the edge of a black hole isn’t normal. There, if these pairs of particles blip into existence, it’s possible for one side of the pair to fall in. “The one that falls into the black hole effectively has negative energy,” Burgess says, “and the other one can get out and escape from the black hole, with positive energy.”
The particle that escapes forms the Hawking radiation. And since the particle that falls in has negative energy, “you’re essentially subtracting energy from the black hole,” Burgess says. “It means you’ve taken mass away from the black hole.”
Now, no physicist has ever directly witnessed this happening (a quirk of the theory is that smaller black holes, which are harder for astronomers to find, will radiate more heat). But Hawking’s math was so convincing that just about every physicist believes this radiation exists. And that means that black holes eventually evaporate and even explode.
The finding was so important because, first off, it provided a clue that one day, quantum mechanics and general relativity could be united into one grand theory. In other words, if quantum mechanics and relativity could come together to explain what the hell is happening at the edge of a black hole, they could probably come together elsewhere.
But it also prompts other hugely interesting, unanswered questions about black holes. “For one, Hawking radiation seems to do things that should be impossible,” Burgess says, like delete all information about what went into the black hole.
If you fill up a black hole with solid gold, and fill up another one with pizzas, the Hawking radiation that each black hole emits will be the same. That actually breaks the laws of the universe as we know them.
Quantum mechanics states that you ought to be able to completely account for the path of any particle in the universe. So if you throw a pizza into a black hole, you should be able to trace how that pizza is torn apart; you should be able to see what happens to the individual atoms that constitute the crust, the cheese, etc. Quantum mechanics stipulates that all particles in the universe can be accounted for and information cannot be deleted.
But in a black hole, that information is lost. Hawking radiation means the black hole is losing mass. But we have no idea what that means for the pizza, which, presumably, is still inside the black hole.
It’s a scientific mystery that questions one of our most basic laws of nature. And Burgess says Hawking radiation continues to generate questions and research into the nature of gravity and how it relates to other forces.
Scientists still don’t have a great understanding of how quantum mechanics (the science of the very small) explains gravity. And Hawking, with his radiation, provided a tantalizing clue.
See:
https://www.vox.com/science-and-hea...0/stephen-hawking-hawking-radiation-explained
Empty space really does have quantum fields all throughout it, and those fields really do have fluctuations in their energy values. There’s a germ of truth in the “particle-antiparticle pair production” analogy, and it’s this: in quantum field theory, you can model the energy of empty space by adding up diagrams that include the production of these particles. But it’s a calculational technique only; the particles and antiparticles are not real but are virtual instead. They are not actually produced, they do not interact with real particles, and they are not detectable by any means.
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