Albert Einstein’s General Theory of Relativity explains the structure of spacetime, or how spacetime curves according to mass. For example, our sun distorts the space around us in such a way that the earth rolls around the sun like a marble thrown into a funnel (the earth’s lateral momentum prevents it from falling into the sun). yeah).

Proposed in 1915, the theory was revolutionary at the time, reconsidering gravity as the curvature of spacetime. As much as the theory is fundamental to the very nature of the space around us, physicists say it may not be the end of the story. Instead, they argue, the secret of how our universe works at its deepest level is hidden in the theory of quantum gravity, which seeks to unify general relativity and quantum physics. ing.

One place to look for imprints of quantum gravity is in powerful collisions between black holes where gravity is at its most extreme. Black holes are the densest objects in the universe. Its gravity is so strong that it crushes falling objects into spaghetti-like noodles. When two black holes collide and merge with one large object, the space-time around them is disrupted, sending ripples called gravitational waves outward in all directions.

Funded by the National Science Foundation, managed by the California Institute of Technology and the Massachusetts Institute of Technology, LIGO has been regularly detecting gravitational waves produced by merging black holes since 2015 (with its partner observatories Virgo). KAGRA participated in this exploration in 2017 and 2020 respectively). But so far, general relativity has passed test after test, and shows no signs of breaking down.

Now, two new papers led by the California Institute of Technology, *Physical Review X* and *physical review letter*, describes a new way to put general relativity to a more rigorous test. By looking more closely at the structure of black holes and the space-time ripples they produce, scientists are looking for signs of small deviations from general relativity that suggest the existence of quantum gravity.

“When two black holes merge to produce a larger black hole, the final black hole rings like a bell,” said Caltech professor of physics and co-author of both studies. Yanbei Chen (Ph.D. 2003) explains. “If a particular theory of quantum gravity is correct, the quality of the ringing, or its timbre, may differ from that predicted by general relativity. It’s designed to look for differences in sounds, such as overtones.”

The first paper, led by Caltech graduate student Dongjun Lee, explores how black holes roar within a particular framework of quantum gravity theory, or what scientists call supergeneral relativity. We report a new single equation that explains

The research is based on groundbreaking equations developed 50 years ago by Saul Toikorski, Ph.D. ’73, Robinson Professor of Theoretical Astrophysics at Caltech. Toikolsky developed complex equations to better understand how ripples in space-time geometry propagate around black holes. In contrast to numerical relativity, in which a supercomputer must simultaneously solve many differential equations related to general relativity, the Toikolski equation is much easier to use and, as Lee explains, a Provides direct physical insight.

“If you want to solve all the Einstein equations for black hole mergers and simulate them accurately, you have to rely on supercomputers,” Lee says. “Numerical relativity is very important for accurately simulating black hole mergers and provides an important basis for interpreting the LIGO data. The Toikorski equation gives us an intuitive view of what is happening in the ringdown phase.”

Lee was the first to successfully take the Toikolsky equation and apply it to black holes in the realm beyond general relativity. “Our new equations allow us to model and understand gravitational waves propagating around black holes more exotic than Einstein predicted,” he says.

The second paper states *physical review letter*A research team led by Sizheng Ma, a graduate student at Caltech, describes a new way to apply Li’s equation to real-world data that LIGO and its partners will acquire in their upcoming observations. This data analysis approach uses a series of filters to remove the black hole ringing signature predicted by general relativity, revealing potentially subtle, beyond-general relativity signatures. can do.

“In the data collected by LIGO, Virgo, and KAGRA, we can look for features described by Dongjun’s equation,” says Ma. “Dong Jun found a way to transform a large complex equation into just his one equation, which is very helpful. This equation is more efficient than the method we used before It’s handy and easy to use.”

The two studies complement each other well, says Li. “I was initially worried that the features the equation predicted would get buried under multiple overtones and undertones. Fortunately, Sizheng’s filter can remove all of these known features. So we can focus on just the differences,” he says.

Chen added, “By working together, Li and Ma’s research results can greatly enhance the gravitational exploration capabilities of our community.”

**For more information:**

Dongjun Li et al., Perturbation of rotating black holes beyond general relativity: the modified Toikorsky equation, *Physical Review X* (2023). DOI: 10.1103/PhysRevX.13.021029

Sizheng Ma et al, Black hole spectroscopy with mode cleaning, *physical review letter* (2023). DOI: 10.1103/PhysRevLett.130.141401

**Magazine information:**

physical review letter

Physical Review X