The reverberating ring of black hole mergers could help put Einstein theory to test

The papers, published in Physical Review X and Physical Review Letters, focus on the rings of black holes. These don't refer to the characteristic accretion discs of black holes, but to the gong-like ring of black holes when they crash into each other during a merger.

"When two black holes merge to produce a bigger black hole, the final black hole rings like a bell," Yanbei Chen, a professor of physics at Caltech and a co-author of both studies explained in a press statement. "The quality of the ringing, or its timbre, may be different from the predictions of general relativity if certain theories of quantum gravity are correct. Our methods are designed to look for differences in the quality of this ringdown phase, such as the harmonics and overtones, for example."

The first of the two new papers details a new single equation that describes how black holes would ring based on specific quantum gravity theories. The work builds upon an equation developed 50 years ago by Saul Teukolsky at Caltech, which simplified the process of understanding how space-time geometry is affected by black holes.

"If one wants to solve all the Einstein equations of a black hole merger to accurately simulate it, they must turn to supercomputers," said Dongjun Li, graduate student, and co-lead of the new paper. "Numerical relativity methods are incredibly important for accurately simulating black hole mergers, and they provide a crucial foundation for interpreting LIGO data. But it is extremely hard for physicists to draw intuitions directly from the numerical results. The Teukolsky equation gives us an intuitive look at what is going on in the ringdown phase."

"Our new equation allows us to model and understand gravitational waves propagating around black holes that are more exotic than Einstein predicted," he continued.

Detecting signals related to quantum gravity

The second paper, meanwhile, describes a method for applying Dongjun's equation to gravitational wave data acquired by the Laser Interferometric Gravitational-Wave Observatory (LIGO), which recently started its fourth observation run.

The new method uses filters to remove features of a black holes' ringing that are predicted by general relativity. By doing this, the scientists hope they will be able to detect subtle signatures that are related to quantum gravity.

"I was initially worried that the signatures my equation predicts would be buried under the multiple overtones and harmonics; fortunately, Sizheng's filters can remove all these known features, which allows us to just focus on the differences," Dongjun said.

"Working together," Chen added, "Li and Ma's findings can significantly boost our community's ability to probe gravity."