Hawking’s Black Hole Theorem Confirmed Observationally for the First Time

An artist’s impression of two black holes about to collide and merge.

Study offers evidence, based on gravitational waves, to show that the total area of a black hole’s event horizon can never decrease.

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 (July 1, 2021) 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.

Physicists at MIT and elsewhere have used gravitational waves to observationally confirm Hawking’s black hole area theorem for the first time. This computer simulation shows the collision of two black holes that produced the gravitational wave signal, GW150914. Credit: Simulating eXtreme Spacetimes (SXS) project. Credit: Courtesy of LIGO

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.

An age of insights

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.

Before and after

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.”

Reference: “Testing the Black-Hole Area Law with GW150914” by Maximiliano Isi, Will M. Farr, Matthew Giesler, Mark A. Scheel and Saul A. Teukolsky, 1 July 2021, Physical Review Letters.
DOI: 10.1103/PhysRevLett.127.011103

This research was supported, in part, by NASA, the Simons Foundation, and the National Science Foundation.

AstronomyAstrophysicsBlack HoleGravitational WavesLIGOMITPopular
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  • Eric Bright

    How can this AND Hawking’s radiation be true at he same time? Aren’t they contradicting each other? If one is true, the other has to be false.

    • Torbjörn Larsson

      Hawking radiation is so small it can be ignored in large BHs, so the contradiction doesn’t really exist for the BH’s or BH mergers detected by LIGO.

      • Alex

        The theorem has got nothing to do with Hawking radiation.

  • Eric Bright

    Alternatively, If both are to be true, then no black hole can ever radiate out of existence (as is commonly believed to happen given enough time if Hawking’s radiation actually happens). They might radiate up to a point, and not any further.

    • Torbjörn Larsson

      Physicists have speculated in BH relicts, but not for the reason you mentioned but because there are problems with describing evaporating BH physics in full.

  • Eric Bright

    Indeed, the Hawking’s radiation, if this theorem to be held true, has to always keep a black hole shrinking (which is not totally clear why, when each emerged-pair can randomly be spared or trapped, nullifying any mass loss by equal amount of mass gains). Therefore, if I understood them correctly, a black hole can never evaporate out of existence, ever. Once all the surrounding matters are vacuumed and there is nothing left to fall into it, the Hawking’s radiation keeps adding and subtracting mass to and from the black hole ad infinitum, without the black hole losing any mass. If the black hole loses any mass, then it violated that Hawking’s theorem, since the event horizon has to shrink as a result, inevitably. What am I missing here? Help!

    • Aleksandr7364

      You lack the correct theory in which the Center of the Universe synthesizes (gives birth to) all the centers of galaxies, the centers of galaxies synthesize stars, and stars synthesize planets.
      https://www.youtube.com/watch?v=tFUM3vAlaGc

        • Aleksandr7364

          Terms like “dark matter, dark energy, black holes, the Big Bang, crooked space, crooked time” are time to throw away in the dustbin of history, along with all the noodles that have grown over the last 100 years around these erroneous terms.
          There are 4 types of long-known stable matter:
          1) strings located in the Center of the Universe;
          2) quarks located in the centers of galaxies;
          3) nucleons that are in the stars;
          4) atoms in the planets.
          Each type of matter has its own gravity (reactive thrust of electromagnetic waves)
          1) the gravity of the strings pulled the strings from a diameter of 2 * 10 ^ 28 light years in the Center of the Universe and started the synthesis of quarks for the centers of galaxies. It is 10 ^ 28 times stronger than the earth;
          2) the gravity of quarks keeps galaxies in orbits around the Center of the Universe. It is 10 ^ 18 times stronger than the earth;
          3) the gravity of nucleons keeps stars in orbits around the centers of galaxies. It is 10 ^ 6 (million) times stronger than Earth.
          4) the gravity of atoms holds planets as well as comets and asteroids in orbits around stars.
          All types of gravity do not interact with each other (have different frequencies) – the Center of the Universe does not attract stars, and the centers of galaxies do not attract planets, people, dust and gas …

          • Torbjörn Larsson

            ? Eric Bright is asking relevant questions, but you respond with nonsensical and self promoting pseudoscience claims. Please don’t do that!

    • Torbjörn Larsson

      I’m not sure what you are asking here. Hawking radiation is not yet observed directly but in analogous systems based on sounds and trapped surfaces in flowing liquids – its existence is a simple consequence of semiclassical physics where you apply wavefunctions of other fields to trapped surfaces (that GR can make, such as the event horizon). See the original papers for the physics and explanations.

      You seem to worry about small black hole evaporation, which is a problem, but has nothing to do with the mechanism of Hawking radiation in the first place.

    • Michael pace

      So for some apparent reason this particular article aswell as all of the comments made as to what peoples own opinions are concerning this specific topic about black holes is indeed very very interesting but in all actuality everything that has been noted aswell as spoken about is all just theories and opinionated thoughts without any “REAL” evidence that any of hawkings aswell as Einstein thoughts,ideas,and research isnt anything other than simply just a theoretical thesis…although I am speaking on a matter than I don’t know much about I am very intrigued to say the least but I am quite sure that myself and others around the world who are fascinated with space and with the way things work with nature and the laws of physics would really like to see some promising proof that this hypothesis that was created many years ago is more than just an opinionated theory..I am very curious to know as to how or why any of these theories were ever created in the first place and how was any of that ever relevant with how things work within our galaxy..so according to what I’ve read specifically and if I am understanding everything correctly black holes could very well be like a glitch in the time continuem that we know and abide by here on our small planet in this one galaxy and with the way they rotate and with the very very strong gravitational pull that they apparently have then that would mean that they exist so that things in our galaxy stays in motion and rotates properly in order around the sun the way each and every single planet does am I somewhat on the right track here or am I completely wrong but then again since everything that has been previously mentioned and researched and studied is all just a theoretical hypothesis that doesn’t have any concrete proof anyways so what im saying in my opinion isn’t right or wrong its but rather a well educated guess along with theories and opinions of my understanding aswell as a creative imaginative thought process..so if black holes supposedly don’t ever dissipate or evaporate or shrink in size unless 2 come together and form another initial black hole which alternatively winds up being larger than the previous 2 and according to the theories that I’ve researched and read myself that anything that gets sucked into that it basically gets destroyed,annihilated and supposedly would never cease to exist again correct??but again this is all just theoretically speaking because there isn’t anyone on the face of this earth presently and also of the past that can actually prove any of this to be true because idk about you but from what I have gathered about all of this being that these “black holes” are many many light-years away which meaning that its not possible for any human to ever obtain any concrete proof as to if these things actually exist because well as a human we only live for so many years and would die long long before ever making it anywhere near one of these things to actually be able to vouch and say that these are things that actually do exist…anyways I apologize for the rambling and I don’t ever do anything like this but this caught my attention and intrigued me and I just figured I would comment my own personal thoughts on the theory and im just a 32 year old man with a high school education lol..If anyone has any thoughts or feedback to anything I have said I would love to hear anyone’s opinions thanks

  • anon

    The issue with Hawking radiation is that for every quantum particle-antiparticle pair that spontaneously emerges from the quantum fizz (as I like to call it), there will be some (not all) cases where one particle is pulled into the event horizon and the other particle escapes. This will not occur anywhere except near yet still outside the event horizon of a black hole to particular mathematically definable conditions. Furthermore, the exact expected rate of Hawking radiation can therefore also be calculated with this in mind, although it could still (and likely is) affected by certain conditions, such as rotation of the black hole because it will quite literally drag spacetime along behind it. Since the surface area for one should remind constant (where I’m guess Hawking radiation will actually slowly shrink it over time), this means that the shape of the event horizon will affect the chances of one particle escaping. A flatter horizon with fewer perturbations due to spin would produce a higher rate of evaporation. In addition, a smaller black hole evaporates faster, as more of those possible directions near the event horizon point outward, as the convex curvature of the space is more pronounced. Once the threshold is reached and the event horizon can no longer sustain itself, the resulting explosion of material would be so violent that if one made a micro-black hole on Earth in a lab that were microscopic, it would not only annihilate the Earth out of any recognizable form, but it would quite likely also blow up the moon. So no one is going to try making one anywhere near the Earth even if they could.

    There are many, many laws in the universe, and they all mess with each other because they are all happening at the same time. That is the primary reason why science is challenging.

    • Torbjörn Larsson

      As I noted in another comment, people are looking for testing Hawking radiation. Hawking radiation is not yet observed as such but in analogous systems based on sounds and trapped surfaces in flowing liquids and, as here, flowing gas: https://phys.org/news/2021-02-stationary-hawking-analog-black-hole.html .

      As you yourself say evaporating black holes evaporate ever faster, and that is because they heat up and thus the radiation intensity goes up.

      Vacuum pair production is not particles of resonant quantum field ripples but “virtual particle” pairs of non-resonant ripples [ https://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/ ]. It is IIRC the event horizon which acts like a particle prompting real pair production from a passing high energy photon. But you can use other simplistic models such as the Unruh effect (an accelerating observer will observe a thermal bath, like Hawking blackbody radiation, near an event horizon).

  • John Campbell

    Like universal expansion, this is unverifiable, meaningless bullsh*t.

  • Alex

    LOL… 1971 was a mere 50 years ago. The “OBSERVED” event is how many LIGHT YEARS away? Check back with us in 10,000 years or so, for proof of concept. These are Presumptions, akin to looking at a tintype photograph from 140 years ago, at a distance of Earth-to-Pluto… PRESTO CHANGE-O! ONE “diagnoses” an “apparent” skin condition present on (what APPEARS to be) the left earlobe of the (presumed) FEMALE subject… The ultimate CONCEIT of Science, is in-and-of an UNPROVED UNIVERSE. It is the same SCIENCE chasing the BUCK at the expense of CAUTION… and the very NATURE of Science itself. MAYBE, if Science had done a RESPONSIBLE job of throttling the misuse of its insight(s), it might have my respect but… THAT’S NOT YOUR JOB, OR YOUR PROBLEM. You exist in a moral and ethical “black hole”, a VOID of rationalization which “spins” like the proverbial whirlwind…the World will inherit the HURRICANE.
    TO WIT:
    As observed above by others, Hawking’s theories are self-contradictory, and INTRORSE in their “LOGIC”: Theory based on assumption, based on “prescribed” MATHS. Shaky ground: overall INSIGHTS, Medieval in character for what is EXCLUDED. ORTHODOXY, in other words. You can keep it to yourself. Get back to me when you have something RELEVANT to say about what is REAL… like, REPAIRING the deplorable state of the Earth.

    I am not now, nor have I ever been a LUDDITE. Back into swords…

    Oh yeah 😳… whatever became of those “microscopic” black holes that “fell through” the containment chamber at the CERN facility, back a few years? Not that there’s anything WRONG with that. It was just ANOTHER one of Alex’s No-good, Very-bad days…
    🦋

    • topheR

      Omg Alex, you’re so right. Your superior intellect shines through your excellent writing and you’ve convinced me that science is bunk and that we should all renounce it entirely and just follow you around in hopes that you’ll drop more occasional pearls of life-changing wisdom. What’s next, Fearless Leader? Where do we go from here, now that we’re free of all that silly science buffonery?

    • Torbjörn Larsson

      Relevance? Astronomers used the reference frame of “now” for their observations – the redshift is a convenient distance measure for these near universe evenst that happens all the time.

      Also, why the crackpot font!? How is that going to entice people to read your future comments past the here first, erroneous sentences showing that you don’t know what you comment on? First you must learn that, then you should try to learn how to write sensibly too.

  • BibhutibhusanPatelq

    This is a fact of common experience that when any two bodies added to mix togather then thired body formed is larger than previous two taken single and single.ĺs there any law present for super massive blackholes addìtion.Or doès Einstein’s theory holds beyond our milkyway.So,these are simply eýe speculations9 having no spctular calculation,that any one can boost.

    • Torbjörn Larsson

      That is the general expectation but black holes are a new type of systems that little was known about. This is one of the first derived properties, and it took several decades to check it at a measly 2 sigma – we need to check further (want a 5 sigma observation).

  • BibhutibhusanPatelq

    This is a fact of common experience that when any two bodies added to mix togather then thired body formed is larger than previous two taken single and single.ĺs there any law present for super massive blackholes addìtion.Or doès Einstein’s theory holds beyond our milkyway.So,these are simply eýe speculations9 having no spctular calculation,that any one can boost.Each and every galaxy is rotating relative to others besides moving away from one another which is nòt at all constant and homogeneous.Hence laws applied in the frme of referrence of our milky way dò not hold for other galaxies.But on some few cases may approximate results be calculated.qa

  • Nasir

    Nice but how can I get it cozy just want to know

  • Elto D

    In reply to Bibhu.. if you merge 2 spheres of equal size into a bigger sphere, the area of the resulting sphere is quite smaller than the sum of the areas of the 2 initial spheres. So the case of merging black hole is different, and not trivial.

    • Torbjörn Larsson

      That is an even better observation and response. Sorry, I hasted and wrote my own response first – which was not as good.

  • Torbjörn Larsson

    They are able to extract black hole masses and spins before and after, and test the law at 2 sigma – the main take home is that it is now a doable observation but needs more data.

    Interesting expansion on recent tests of the black hole no-hair-theorem – we are learning fast now!

  • BibhutibhusanPatel

    Exactly the collision of super massive black holes follow law of conservation of mass,so surface area does not decrease.But the the equations are due to Hawkings.Thanks to the authors for verification and mostly for observation.

  • BibhutibhusanPatel

    The collision of two super massive black holes follows the law of conservation of mass.So the total surface areas added togather do never decrease as this is directly proportional to mass.However excess surface area is geneŕated from the momentum as law of conservation of
    momentum follows before and after collision.Sò this proves in turn mass-radius relationship for super massive bĺackholes.

  • S

    So if a black hole can’t shrink in size and doesn’t release anything from its grasp, then how does entropy whittle away at it?

  • Wonderingman

    Just wondering: is it possible the event horizon never shrinks but the bh itself does? Iow, as hawking radiation is released some system is in effect which maintains the size of the EH while the BH decreases in mass?

  • Girl 1

    So I’m not a genius like all of you…but just know I’ve been completely entertained by you guys banter and thanks to the person who pasted about the 4 types of matter…I’m going to read more about that I was sad to know I hadn’t been taught about it and that its not common knowledge.

    • Aleksandr7364

      Thank you. I was glad to help.

  • John

    Two objects merge and the result is a bigger object. What a fantastic observation. Billions of dollars well spent. Congratulations.

  • Garrett

    How about sending a drone into the black hole to see whats on the other side