/Fresh analysis of LIGO data supports “no hair” theorem for black holes

Fresh analysis of LIGO data supports “no hair” theorem for black holes


A night sky interrupted by two black voids.
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/ Simulated image of two merging black holes detected by LIGO, viewed face-on.

Physicists have “heard” the telltale ring of an infant back hole for the first time, thanks to a fresh analysis of LIGO data. Researchers specifically looked for telltale “overtones” in the data from the collaboration’s Nobel Prize-winning detection of two black holes merging. Not only were the overtones present, but the pattern of pitch and decay matches predictions for the black hole’s mass and spin derived using the general theory of relativity. According to a new paper in Physical Review Letters, the result also supports the so-called “no hair” theorem for the classical description of black holes.

That classical picture of a black hole is a circle with a dot at the center. The circumference of the circle is the event horizon, and the dot is the singularity. General relativity holds that the area of the event horizon is a vacuum with no structure. That’s because any dust, gas, or elementary particle placed at the horizon should fall into the black hole, maintaining the vacuum state. There would be no noticeable change if you threw something into a black hole—nothing that would provide a clue as to what that object might have been. It was the late physicist John Wheeler who coined the colorful description, “Black holes have no hair.” (Wheeler had a knack for catchy names and phrases.) So all you need to describe black holes mathematically is their mass and their spin, plus their electric charge.

“We all expect general relativity to be correct, but this is the first time we have confirmed it in this way,” said lead author Maximiliano Isi of MIT. “This is the first experimental measurement that succeeds in directly testing the no-hair theorem. It doesn’t mean black holes couldn’t have hair. It means the picture of black holes with no hair lives for one more day.”

“The picture of black holes with no hair lives for one more day.”

General relativity also predicts that two merging black holes should give off powerful gravitational waves—ripples in the fabric of spacetime so faint, they are very difficult to detect. LIGO is able to do so via laser interferometry, using high-powered lasers to measure tiny changes in the distance between two objects positioned kilometers apart. LIGO has detectors in Hanford, Wash., and in Livingston, La. A third detector in Italy called Advanced VIRGO came online in 2016. Each instrument is so sensitive that it also picks up small ambient vibrations, like a rumbling freight train or natural thermal vibrations in the detectors themselves. So the LIGO collaboration goes to great lengths to shield its instruments and minimize noise in its data.

On September 14, 2015, at 5:51am EST, both detectors picked up signals within milliseconds of each other for the very first time. The waveforms of those signals serve as an audio fingerprint—in this case, evidence for two black holes spiraling inward toward each other and merging in a massive collision event, sending powerful shock waves across spacetime. Picking up the signals was a stunning achievement, and nobody was surprised when the first direct observation of gravitational waves won the 2017 Nobel Prize in Physics.

An upgraded LIGO is still detecting various other candidate events. While there have been some naysayers casting doubt on that first event, two independent studies confirmed the detection last year, so the controversy has been largely laid to rest.

Overtones in the ringdown

LIGO detected a telltale “chirp” pattern in the data as the two black holes spiraled into each other before merging to form a new black hole. That new black hole should have vibrated from the force of that impact, and those vibrations—called a “ringdown”—should also have produced gravitational waves. But physicists had assumed the vibrations would be far too weak for LIGO’s instruments to detect right now, given all the noise from the initial collision.

Study co-author Matt Giesler, a graduate student at Caltech, realized that this pessimism was caused by a focus on the main vibrational frequency. But that’s not the only signal present. The gravitational-wave signal should have multiple frequencies that fade away at different rates (decay), with each tone corresponding to a vibrational frequency of the new black hole.

“There’s not a single tone, there’s actually many tones that make up this ringdown signal,” Giesler said. “We realized that one of these extra tones should be visible in the existing data that’s public.” If present, they should yield accurate estimates of the mass and spin of the new black hole.

Having those additional tones also makes it possible to test the “no-hair” theorem, which requires two independent measurements to confirm mass and spin. “People had this idea of doing the test, but they always thought in terms of using the so-called fundamental tone,” said co-author Saul Teukolsky, a physicist at Caltech and Cornell University.

Illustration of the "overtones" in the ringing signature of a newly formed black hole.
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/ Illustration of the “overtones” in the ringing signature of a newly formed black hole.

M. Isi/Massachusetts Institute of Technology

Giesler tried performing the test with simulated data. He found he could detect the overtones in the last few milliseconds of the signal, just after the telltale chirp’s peak, and reported his results to Teukolsky.

“I got very excited and said, ‘We need to try this on the real data,'” said Teukolsky. Sure enough, they were able to identify two distinct tones in the data and measure the pitch and decay of each. Their calculations matched previous measurements of the black hole’s mass and spin.

“To be quite honest, this is the first time this has been done, and it’s not a very strong test,” added Teukolsky, noting error bars on the measured frequencies and damping times. “It was really more to show that it can be done. People thought we would have to wait 15-20 years, maybe even for detectors in space, before the precision of the detectors would be good enough to look for this effect. We’ve shown we can start doing it now. As the precision of the detectors improves over the next few years, these tests should get better.”

Proof of principle

Now that proof of principle has been established, the physicists will try hunting for the overtones in the data from other events detected by LIGO. But there is no guarantee of success, even with the marked improvements to the detector since 2017.

“That first detection is still the strongest signal that’s been seen so far,’ said Prof. Teukolsky. “We have to see another one at least as good as that.” And for that, they’ll have to depend on the whims of nature.

“The bigger and louder an event, the more likely LIGO can pick up these overtones,” said Caltech physicist Alan Weinstein, a member of the LIGO Laboratory, who is not a co-author on this latest study. “With LIGO’s first detection of gravitational waves, we confirmed predictions made by general relativity. Now, by searching for overtones and even fainter signals called higher-order modes, we are looking for deeper tests of the theory and even potential evidence of the theory breaking down.”

For instance, “Black-hole spectroscopy could one day rule out the possibility that what we think of as black holes are actually black hole ‘mimickers’—conjectured compact objects like boson stars or gravastars that lack an event horizon,” Marric Stephens wrote at APS Physics. “Their properties would show up as deviations from the ringdown signatures predicted by general relativity.” In other words, such objects might not “ring” in quite the same way, giving physicists a chance to spot them.

The work demonstrates yet again how useful LIGO’s data can be for investigating many kinds of challenging questions in physics. “It’s great that all the data is made public,” said Teukolsky, even though his group is part of the LIGO collaboration and would have had access regardless. “Really, anybody could have taken the data from that first event and done this analysis.”

DOI: Physical Review Letters, 2019. 10.1103/PhysRevLett.123.111102 (About DOIs).