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For whom the black hole rings

First strong observational evidence for multimode ringdown in a binary black hole collision

August 31, 2024

An international team led by researchers from the Max Planck Institute for Gravitational Physics (Albert Einstein Institute, AEI) in Hannover has found the first strong observational evidence for multiple gravitational-wave frequencies in a binary black hole ringdown. The team discovered that the intermediate-mass black hole formed in the GW190521 event vibrated briefly at at least two frequencies after the merger. This ringdown is a fundamental prediction from general relativity. Its observation allows tests of the theory and of the black hole no-hair theorem. The scientists found no violations of the theorem or deviations from general relativity. It was widely assumed that this observation would be impossible before the next generation of gravitational-wave detectors. The results were published in Science today.

When two black holes collide, gravitational waves are emitted in three phases: when they inspiral, when they merge, and when the newly formed initially lopsided black hole settles into its final stage. The last phase, called “ringdown”, is a fraction-of-a-second period of black hole vibrations that – according to Einstein’s theory of general relativity – encode information about the mass and the spin of the final black hole.

A black hole rings like a bell

“The black hole is similar to a rung bell, which produces a spectrum of multiple fading tones, that encode information about the bell,” explains Collin Capano, researcher in the Observational Relativity and Cosmology department at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute, AEI) in Hannover and corresponding author of the study published in Science today.

An international team led by researchers from the AEI Hannover analyzed public LIGO and Virgo data from the GW190521 event, the binary black hole merger with the highest total mass observed to date. They discovered a chord of two damped tones (also called “quasi-normal modes”) present in the gravitational waves emitted during the ringdown phase of the event.

First multimode observation in a black hole ringdown

“This is the first time a multimode observation – in other words, the detection of two vibration frequencies of a deformed black hole – has been achieved. It was widely assumed this would not be possible before the next generation of gravitational-wave detectors,” says Capano.

The researchers performed an agnostic search for the frequencies present in GW190521’s ringdown. They searched for individual fading tones and did not assume any relation between the modes’ frequencies and their damping times. They identified two modes: A fundamental mode at a frequency of 63 Hertz and a sub-dominant one at 98 Hertz with damping times of 26 milliseconds and 30 milliseconds, respectively. These measurements agree with numerical relativity simulations of black hole collisions.

No hair on GW190521

The no-hair theorem states that in general relativity black holes are completely characterized by three externally accessible quantities: their mass and their spin, and their electric charge, which vanishes for astrophysical black holes. No further information, or additional “hair” is required to described them. The frequencies of the ringdown modes and their damping times of the black hole formed in GW190521 must therefore be determined by mass and spin only.

Numerical simulation of a heavy black-hole merger (GW190521)


“We tested the black hole no-hair theorem by comparing the frequencies and the damping times of the two modes we found in the GW190521 ringdown,” says Julian Westerweck, a PhD student in the Observational Relativity and Cosmology department at AEI Hannover and co-author of the publication. “Reassuringly, GW190521 passed the test and we found no signs of any black hole physics beyond Einstein’s general theory of relativity.”

The research team assumed that the frequency and decay time of the fundamental vibration mode of the black hole depend on its mass and spin as predicted by Einstein’s theory. They allowed the frequency and decay time of the second mode they found to deviate from the values expected in general relativity and checked how well such deviations fit the observations. Their analysis showed the absence such deviations and that GW190521 is consistent with Einstein’s theory.

“We can now also lay to rest two alternative proposals about the somewhat mysterious nature of GW190521,” says Badri Krishnan, group leader at AEI Hannover and professor at Radboud University. “Both a head-on collision of exotic stars and the collapse of a massive star to a black hole with a high-mass disk are excluded now, as they are not compatible with the observed multimodal ringdown.”

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