# Physicists should listen carefully to the ring of black holes

Albert Einstein’s General Theory of Relativity describes how the fabric of space and time, or space-time, curves in response to mass.

Our sun, for example, distorts the space around us so that planet earth rolls around the sun like a marble thrown into a funnel (earth does not fall into the sun due to earth’s sideways motion).

The theory, which was revolutionary at the time it was introduced in 1915, formulated gravity as a curvature of space-time.

As fundamental as this theory is to the nature of the space around us, physicists say this may not be the end of the story.

Instead, they argue that theories of quantum gravity, which attempt to unify general relativity with quantum physics, hold secrets about how our universe works at the deepest levels.

One place to look for signatures of quantum gravity is in the violent collisions between black holes, where gravity is at its most extreme.

Black holes are the densest objects in the universe – their gravity is so strong that they crush objects falling into them into spaghetti-like noodles.

When two black holes collide and merge into one larger body, they spin spacetime around them, sending ripples called gravitational waves outward in all directions.

Funded by the National Science Foundation and managed by Caltech and MIT, LIGO has been routinely detecting gravitational waves produced by black hole mergers since 2015 (its partner observatories Virgo and KAGRA joined the hunt in 2017 and 2020, respectively).

So far, however, general relativity has passed test after test without showing any sign of collapsing.

Now, two new Caltech-led papers, Physical Review X and Physical Review Letters, describe new ways to put general relativity to even more rigorous tests.

By looking more closely at the structure of black holes and the ripples they produce in spacetime, scientists are looking for signs of small deviations from general relativity that would indicate the presence of quantum gravity.

“When two black holes merge and a larger black hole is formed, the final black hole rings like a bell,” explains Yanbei Chen (PhD ’03), professor of physics at Caltech and co-author of both studies.

“The quality of the sound, or its timbre, may differ from what General Relativity predicts if certain theories of quantum gravity are correct. Our methods are designed to look for differences in the quality of this decay phase, such as the harmonics and overtones.”

The first paper, led by Caltech graduate student Dongjun Li, reports a new single equation that describes how black holes would sound in the framework of certain theories of quantum gravity, or what scientists call the regime beyond general relativity.

The work builds on a pioneering equation developed 50 years ago by Saul Teukolsky (PhD ’73), Caltech’s Robinson Professor of Theoretical Astrophysics. Teukolsky had developed a complex equation to better understand how ripples in space-time geometry propagate around black holes.

Unlike numerical relativity methods, which require supercomputers to simultaneously solve many differential equations of general relativity, Teukolsky’s equation is much easier to use and, as Li explains, offers direct physical insights into the problem.

“If you want to solve all of the Einstein equations of a black hole merger to accurately simulate it, you have to resort to supercomputers,” says Li.

“Numerical relativity methods are incredibly important for accurately simulating black hole mergers and provide a critical basis for interpreting LIGO data. However, it is extremely difficult for physicists to draw direct conclusions from the numerical results. The Teukolsky equation gives us an intuitive insight into what is happening in the ringdown phase.”

Li was able to adapt Teukolsky’s equation for black holes beyond general relativity for the first time. “Our new equation allows us to model and understand gravitational waves propagating around black holes that are more exotic than Einstein predicted,” he says.

The second paper, published in Physical Review Letters, led by Caltech graduate student Sizheng Ma, describes a new way to apply Li’s equation to actual data collected by LIGO and its partners in their next observing run.

This data analysis approach uses a series of filters to remove features of black hole ringing predicted by general relativity, potentially revealing subtle signatures beyond general relativity.

“We can look for features described by the Dongjun equation in the data that LIGO, Virgo and KAGRA will collect,” says Ma.

“Dongjun found a way to translate a large set of complex equations into just one equation, and it’s tremendously helpful. This equation is more efficient and easier to use than the methods we used before.”

The two studies complement each other well, says Li. “Initially I was afraid that the signatures predicted by my equation would be buried under the many overtones and harmonics; Luckily, Sizheng’s filters can remove all of these known features, so we can just focus on the differences,” he says.

Chen added, “By working together, Li and Ma’s findings can greatly increase our community’s ability to explore gravity.”

*Written by Whitney Clavin*