## Understanding Gravity: Scrutinizing The Framework of Spacetime: A Glance at the Past

Albert Einstein’s general theory of relativity is a groundbreaking scientific proposition that deciphers the peculiar concept of spacetime – how it bends and contorts due to mass. To illustrate, our Sun’s gravitational force distorts the spacetime around it, causing the Earth to revolve around the Sun, much like a marble spiralling in a funnel. It’s this intricate dance between mass, gravity, and spacetime that prevents the Earth from being sucked into the Sun, primarily due to Earth’s sideways momentum.

The general theory of relativity, introduced in 1915, revolutionized our perception of gravity by portraying it as a warp in spacetime. Despite being an indispensable cornerstone in understanding the space that envelops us, physicists speculate that it may not encapsulate the entire cosmic picture. They postulate that the theories of quantum gravity, which strive to bridge the gap between general relativity and quantum physics, may hold the key to unfurling the universe’s deepest secrets.

## Unveiling Quantum Gravity: A Collision Course

The quest for quantum gravity’s footprints often leads scientists to the cataclysmic collisions between black holes. Black holes are the densest entities in the universe, possessing a gravitational force so immense that it elongates any object that falls into it into a noodle-like structure. When two black holes collide and amalgamate into a larger entity, they agitate spacetime around them, transmitting gravitational waves that radiate in all directions.

## An Ongoing Investigation: LIGO and the Test of Time

Since 2015, the National Science Foundation-funded LIGO (Laser Interferometer Gravitational-Wave Observatory), supervised by Caltech and MIT, has been regularly detecting gravitational waves produced by black hole mergers. Joined by its partner observatories, Virgo and KAGRA, in 2017 and 2020 respectively, this initiative has yet to find any evidence contradicting the general theory of relativity.

## A Step Further: Probing Quantum Gravity via Black Holes

Two recent studies led by Caltech, featured in Physical Review X and Physical Review Letters, propose novel methodologies to conduct more rigorous tests of general relativity. By scrutinizing the structures of black holes and the spacetime ripples they generate, researchers aim to find minuscule deviations from general relativity that could indicate the existence of quantum gravity.

“When two black holes amalgamate to form a larger black hole, the resultant black hole resonates like a bell,” expounds Yanbei Chen (Ph.D. ’03), a physics professor at Caltech and co-author of both studies. “The resonance quality, or its timbre, may differ from general relativity’s predictions if certain quantum gravity theories hold true. Our methodologies aim to detect differences in this ringdown phase, such as the harmonics and overtones.”

## A Ground-Breaking Equation: Paving the Way for Quantum Gravity Exploration

The first paper, spearheaded by Caltech graduate student Dongjun Li, introduces a unique equation that portrays how black holes would resonate within the realm of certain quantum gravity theories or beyond the general relativity regime.

The research builds upon a trailblazing equation formulated 50 years ago by Saul Teukolsky (Ph.D. ’73), the Robinson Professor of Theoretical Astrophysics at Caltech. Contrary to numerical relativity methodologies that require supercomputers to solve a multitude of differential equations pertaining to general relativity, the Teukolsky equation provides direct physical insight into the problem, simplifying the process significantly.

Li has adapted Teukolsky’s equation to suit black holes within the beyond-general-relativity regime, a pioneering move. “Our novel equation enables us to model and comprehend gravitational waves radiating around black holes that are more exotic than Einstein predicted,” he says.

## Applying the New Equation: Unmasking Gravity’s Mysteries

The second paper, published in Physical Review Letters and led by Caltech graduate student Sizheng Ma, outlines a fresh approach to applying Li’s equation to actual data collected by LIGO and its partners in their upcoming observational run. This data analysis methodology uses a series of filters to eliminate black hole ringing features predicted by general relativity, thereby potentially revealing beyond-general-relativity signatures.

“We can search for features as described by Dongjun’s equation in the data that LIGO, Virgo, and KAGRA will gather,” Ma says. “Dongjun has found a way to condense a large set of complex equations into just one equation, and this is incredibly beneficial. This equation is more efficient and easier to use than previous methods.”

Li and Ma’s studies mutually enhance each other. “I was initially concerned that the signatures my equation predicts would be obscured under the multiple overtones and harmonics; fortunately, Sizheng’s filters can eliminate all these known features, which allows us to focus solely on the differences,” Li says.

Chen concludes, “Together, Li and Ma’s discoveries can significantly enhance our community’s ability to probe gravity.”

Keywords: Einstein’s theory of relativity, LIGO data, Quantum gravity, Black holes, Spacetime, Gravitational waves, Teukolsky equation.

Read Orginal Article: https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.021029