New methods will allow for better tests of Einstein's general theory of relativity using LIGO data

Albert Einstein's general theory of relativity describes how the fabric of space and time, or spacetime, is curved in response to mass. Our sun, for example, warps space around us such that planet Earth rolls around the sun like a marble tossed into a funnel (Earth does not fall into the sun due to the Earth's sideways momentum). 

The theory, which was revolutionary at the time it was proposed in 1915, recast gravity as a curving of spacetime. As fundamental as this theory is to the very nature of space around us, physicists say it might 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 to how our universe works at the deepest levels.

One place to search for signatures of quantum gravity is in the mighty 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 squeeze objects falling into them into spaghetti-like noodles. When two black holes collide and merge into one larger body, they roil space-time around them, sending ripples called gravitational waves outward in all directions.

The National Science Foundation-funded LIGO, managed by Caltech and MIT, has been routinely detecting gravitational waves generated by black hole mergers since 2015 (its partner observatories, Virgo and KAGRA, joined the hunt in 2017 and 2020, respectively). So far, however, the general theory of relativity has passed test after test with no signs of breaking down.

Now, two new Caltech-led papers, in Physical Review X and Physical Review Letters, describe new methods for putting general relativity to even more stringent tests. By looking more closely at the structures of black holes, and the ripples in space-time they produce, scientists are seeking signs of small deviations from general relativity that would hint at the presence of quantum gravity.

"When two black holes merge to produce a bigger black hole, the final black hole rings like a bell," explains Yanbei Chen (Ph.D. '03), a professor of physics at Caltech and a co-author of both studies. "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 paper, led by Caltech graduate student Dongjun Li, reports a new single equation to describe how black holes would ring within the framework of certain quantum gravity theories, or in what scientists refer to as the beyond-general-relativity regime.

The work builds upon a ground-breaking equation developed 50 years ago by Saul Teukolsky (Ph.D. '73), the Robinson Professor of Theoretical Astrophysics at Caltech. Teukolsky developed a complex equation to better understand how the ripples of space-time geometry propagate around black holes. In contrast to numerical relativity methods, in which supercomputers are required to simultaneously solve many differential equations about general relativity, the Teukolsky equation is much simpler to use and, as Li explains, provides direct physical insight into the problem.

"If one wants to solve all the Einstein equations of a black hole merger to accurately simulate it, they must turn to supercomputers," Li says. "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."

Li was able to take Teukolsky's equation and adapt it for black holes in the beyond-general-relativity regime 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 acquired by LIGO and its partners in their next observational run. This data analysis approach uses a series of filters to remove features of a black hole's ringing predicted by general relativity so that potentially subtle, beyond-general-relativity signatures can be revealed.

"We can look for features described by Dongjun's equation in the data that LIGO, Virgo, and KAGRA will collect," Ma says. "Dongjun has found a way to translate a large set of complex equations into just one equation, and this is tremendously helpful. This equation is more efficient and easier to use than methods we used before." 

The two studies complement each other well, Li says. "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," he says.

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

Skyrmion flow control is expected to accelerate the development of next-generation ultra-low-power devices 

In an era marked by an escalating energy crisis, the world stands on the precipice of a transformative revolution in spintronics technology, promising ultra-low power consumption paired with superior performance. To illustrate the potential, consider this: the power consumed by AlphaGo during its famous Go game in 2016 equaled the daily power use of 100 households. By 2021, Tesla's autonomous driving AI required over ten times that amount of power for learning.

In response to this growing demand, the Korea Research Institute of Standards and Science (KRISS, President Hyun-min Park) has pioneered the world's first transistor capable of controlling skyrmions. This breakthrough paves the way for the development of next-generation ultra-low-power devices and is anticipated to make significant contributions to quantum and AI research.

Skyrmions, arranged in a vortex-like spin structure, are unique because they can be miniaturized to several nanometers, making them movable with exceptionally low power. This characteristic positions them as a crucial element in the evolution of spintronics applications.

The explosive growth of electronic engineering in the 21st century can be traced back to the 1947 invention of the transistor at Bell Laboratories in the United States. Acting as an amplifier and switch for electrical currents, the transistor has been pivotal in the field of electronic engineering. The discovery of the skyrmion in 2009 sparked widespread research into a skyrmion-based transistor, but the absence of essential technology to control the skyrmion movement thwarted these efforts.

This bottleneck has been overcome with KRISS's newly developed skyrmion transistor, which leverages proprietary technology to electronically manage the movement of skyrmions created in magnetic materials. This innovative solution enables the precise control of skyrmion flow or halting, akin to how conventional transistors modulate electric current.

A critical aspect of managing magnetic skyrmion movement lies in controlling magnetic anisotropy, which influences the energy of skyrmions. Previous research endeavored to regulate magnetic anisotropy through oxygen movement within devices but failed to achieve uniform control. Overcoming this challenge, the KRISS Quantum Spin Team developed a groundbreaking method for uniform control of magnetic anisotropy by leveraging hydrogen within aluminum oxide insulators, marking a world-first in the experimental implementation of skyrmion transistors.

This milestone represents yet another foundational technology for spintronic devices, following the institute's 2021 achievement in the generation, deletion, and movement of skyrmions. The advent of the spintronics transistor is set to expedite the development of spintronics-based devices, such as neuromorphic and logic devices, which offer substantial advantages in power consumption, stability, and speed over traditional electronic devices.

Dr. Chan Yong Hwang, a director of the KRISS Quantum Technology Institute, expressed, "Major Korean companies are pivoting their focus to next-generation semiconductors that utilize spintronics to transcend the constraints of current silicon semiconductors. We plan to advance spintronics-related technology further and incorporate them into next-generation semiconductor devices and quantum technology."

Reflecting on the significance of the achievement, Dr. Seungmo Yang, a senior researcher at KRISS, stated, "The transistor ignited the digital revolution of the 20th century. Now, the skyrmion transistor is poised to catalyze a similar transformation, propelling the spintronics technology revolution of the 21st century."