Thirty-year mystery of dissonance in the “ringing” of black holes explained

Tokyo, Japan – A scientist from Tokyo Metropolitan University has solved the longstanding problem of a “dissonance” in gravitational waves emitted by a black hole. Using high precision computing and a new theoretical physics framework, it was discovered that it was caused by a resonance between a pair of distinctive “modes” i.e. different ways in which a black hole can “ring.” The phenomenon offers new insights into the nascent field of black hole spectroscopy.

Black holes are astrophysical objects so dense that even light cannot escape their gravitational pull. Despite their awesome presence in the cosmos, however, it is only over the past decade that we have begun to grapple with how they behave. This is thanks to the advent of gravitational wave astronomy, where global detection efforts led by the LIGO (Laser Interferometry Gravitational-Wave Observatory)-Virgo-KAGRA (Kamioka Gravitational Wave Detector) Collaboration have made it possible to detect the disturbances created by black holes in the fabric of spacetime.

Theoretical physicists now face the herculean task of trying to understand the gravitational waves given off by black holes, working from theoretical models. One of these efforts was a calculation made in 1997 by a graduate student, Hisashi Onozawa from the Tokyo Institute of Technology (now Institute of Science Tokyo), who discovered a curious irregularity in what these waves should look like. Just like sound emitted by a ringing bell, gravitational waves are expected to be composed of a combination of “modes,” or different sounds emitted through the different ways in which the black hole “vibrates”. These modes were expected to vary smoothly and predictably. However, the calculations showed a perplexing “dissonance”, where a particular mode behaved completely differently from the others. People at the time suspected a calculation error or an artefact, but even with the advent of better computers, the result remained an unresolved mystery.

Now, after thirty years, Associate Professor Hayato Motohashi from Tokyo Metropolitan University, formerly affiliated with Kogakuin University, has resolved this problem using precision calculations and the nascent theoretical field of non-Hermitian physics. Looking closely at the behavior of modes, he found that the dissonance was not isolated to one mode but was a result of two modes interacting with each other in a resonant fashion. In fact, by examining many modes, it turns out this kind of interaction between modes is not a rare incident, but one which turns up universally in a range of modes.

Through a series of theoretical analyses, this resonance between modes in black holes was shown to be one example of a whole host of physical phenomena in not only astrophysics, but optical physics as well, looking at electromagnetic waves instead of gravitational ones. The interdisciplinary application of a new theoretical approach heralds the birth of the new field of non-Hermitian gravitational physics, unlocking the true potential of global-scale experiments like the LIGO-Virgo-KAGRA Collaboration which are coming online.

This work was supported by JSPS KAKENHI Grant Number JP22K03639.

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