As with many things in the realm of physics, it all began with Albert Einstein. In 1916, the founding IAS Professor predicted the existence of gravitational waves. His theory of general relativity demonstrated that space and time are not fixed coordinates or absolutes, as they were assumed to be in Newtonian physics. And, just as accelerating charges produce electromagnetic waves according to Maxwell’s equations, he concluded that spacetime gets bent and warped by energy, and by the presence of massive objects such as planets. Einstein proposed that these massive objects cause ripples, or waves, to propagate in the fabric of spacetime.
On September 14, 2015, these waves, known as gravitational waves, were detected on Earth for the first time. Since then, scholars from the Institute's School of Natural Sciences have been at the forefront of discovery in this revolutionary field. Working either independently or in small groups, IAS scholars are leading investigations into crucial questions such as the sources of gravitational wave signals, the unexpectedly high frequency of detections, and—extending beyond these direct questions—establishing innovative and unexpected connections between gravitational wave research and particle collider physics. These contributions are pushing the boundaries of knowledge in this field, facilitating the interpretation and analysis of the data currently being gathered, and shaping the trajectory of future discoveries.
What is a gravitational wave?
The clichéd example that can be used to understand the phenomenon of gravitational waves is a bowling ball sitting in the center of a trampoline: the mass of the bowling ball causes the fabric of the trampoline mat to warp, just like spacetime around a planet. Now imagine that you (very foolishly) jump into the center of the trampoline, colliding with the bowling ball. As you crash into each other, both you and the ball would bounce up and down, causing ripples in the trampoline mat. Similarly, if the earth were to collide with an object which has a comparable mass, both the earth and its spacetime curvature would be shaken and ripples in spacetime would result. It is precisely these kinds of oscillations, caused by colliding astrophysical objects such as black holes and neutron stars,1 that are picked up by gravitational wave detectors.
A second analogy is helpful for understanding precisely how gravitational waves are detected: imagine that (having recovered from your collision with the bowling ball) you take a walk around the Institute pond. You throw a pebble into the pond and watch the ripples that travel away from it. Gravitational waves can be understood as the spacetime version of the ripples in the water. Of course, if your colleague, standing on the other side of the pond, also throws in a tiny pebble, the ripples they create might be so tiny that you do not notice them by the time they reach you. But, if they launched an enormous boulder into the water, you would likely detect it at your location. Black hole and neutron star collisions act similarly: they create a huge warping of spacetime in their vicinity which then travels, like the ripples on the water, far enough that we can detect them on Earth.
The gravitational waves that are currently being detected predominantly result from the mergers of black holes—more specifically, black holes that have masses of ten or twenty times that of the sun. However, a few mergers involving neutron stars have also been detected. Each type of merger has a distinct gravitational wave signature. For example, when two neutron stars are merging (each of which is comparable in mass to the sun), the signal detected lasts much longer than that for two black holes. This is because our detectors only notice waves within a limited range of frequencies, and the less massive neutron stars spend more time orbiting each other in the correct frequency range. The first detection of gravitational waves on Earth was made in 2015 by the twin Laser Interferometer Gravitational-Wave Observatory (LIGO).
The first signal, named GW150914, was produced by the merger of two black holes about 1.3 billion years ago. This detection, and those that have followed, has been immensely significant for the study of astrophysics. Gravitational waves provide a new way to observe the universe and study astrophysical phenomena that are largely invisible via other observational methods. They have revealed previously unseen populations of black holes and provide a new understanding of stellar evolution and the building blocks of galaxies.
While black hole and neutron star collisions are confidently identified as the main source of gravitational wave detections, researchers are also seeking other sources of gravitational wave signals that have heretofore gone unrecognized. Member Mor Rozner investigates the effects that the gaseous environments surrounding tightly bound clusters of stars have on gravitational wave outputs. And this is not the only other detection process that scholars have at their disposal; where Rozner’s theories relate to gravitational waves detected by LIGO, Friends of the Institute for Advanced Study Member Gabriela Sato-Polito, Richard Black Professor Matias Zaldarriaga, and past Member and Visitor Eliot Quataert explore gravitational waves that are detected by analyzing the behavior of other stars in the galaxy. Their efforts are directed towards understanding why an unexpectedly high number of gravitational waves have been detected.
Surprisingly, astrophysicists are not the only scholars within the School of Natural Sciences who are taking a keen interest in gravitational wave research. Members Holmfridur Hannesdottir and Sebastian Mizera, whose primary interests are in particle physics, are also contributing to this field. They have identified fundamental mathematical commonalities between black hole collisions and the collisions of particles, providing a valuable tool for the process of analyzing gravitational wave detections. By pursuing these wide-ranging yet complementary lines of inquiry, the School of Natural Sciences is collectively contributing to a tangible transformation of knowledge in this field.
Where are gravitational wave signals coming from?
Through her work, Member Mor Rozner has suggested a major additional source of gravitational wave signals that needs to be accounted for when analyzing data from LIGO: the gaseous environments within globular clusters.
Globular clusters are roughly spherical collections of hundreds of thousands, or even millions, of stars that orbit a common center. They appear with great regularity: there are about 200 globular clusters dotted around the Milky Way, while other galaxies sometimes contain many thousands. At 10–13 billion years old, they are among the oldest objects in the universe.
Rozner describes the traditional picture of these globular clusters as being “very simple.” “For many years,” she says, “people thought that, for globular clusters, there was one burst of star formation and that's it! The cluster is formed.” However, today it is well established that such clusters were not formed in a simple, single event. Instead, clusters are known to consist of multiple star populations that came into being in several distinct episodes.[2] Rozner is interested in the “second population” of stars that formed early on in the cluster’s life. The fact that these second-generation stars are so numerous means that a large amount of gaseous material must have been left over from the first phase of the cluster’s development, in order to provide sufficient raw material for their creation.
In her research, Rozner asks how the presence of this gas might have affected the evolution of a specific type of astrophysical object that exists within the cluster: binary black holes.3 These are pairs of black holes that orbit each other due to their immense gravitational attraction. As Rozner states, “the vast majority of massive objects in the universe are found in binary pairs. So, it's really interesting and, I would say, very important to understand what is going on with these systems.”
As the binary black holes orbit each other, moving closer and closer, they begin to emit gravitational waves. These gravitational waves play a role in the eventual collision and merging of the black holes: the emission of gravitational waves carries energy and angular momentum away from the binary system, causing its orbit to shrink. Eventually, when the black holes get close enough, the gravitational wave emission becomes so intense that the system is rapidly drained of its orbital energy, leading to an unstoppable inspiral that causes the collision.
Rozner’s work adds detail to this picture, highlighting how the surrounding gaseous material within globular clusters also contributes to the evolution of binary black hole orbits. "The gas swirling around the black hole pairs also leeches energy from the system. “That’s another factor helping to make their orbits gradually tighter and tighter over time," she explains.4 Her theory explains that the gaseous environments present during the early stages of globular cluster evolution may have significantly impacted the dynamics of binary systems within them, potentially providing a major, previously unidentified source of gravitational wave signals. While it is unlikely that all gravitational wave signals result from gas-rich globular clusters, the analysis of unique environments such as those considered by Rozner helps to establish a more holistic picture of, in her words, “what's going on in the universe to produce gravitational waves.”
Why are we detecting more gravitational wave signals than expected?
Friends of the Institute for Advanced Study Member Gabriela Sato-Polito, Richard Black Professor Matias Zaldarriaga, and Member (1999–2001, 2023) and Visitor (2005) Eliot Quataert work with gravitational wave data captured by harnessing other stars within the universe as detectors. More specifically, they work with pulsar timing arrays (PTAs). As their name suggests, PTAs involve the observation of pulsars, which are rapidly rotating neutron stars scattered throughout our galaxy.
“Pulsars can be treated like clocks,” says Sato-Polito. “They emit jets of radiation that sweep across space as the star rotates, and they have remarkably stable rotation periods. When these jets pass Earth, we detect, using radio astronomy facilities, a brief pulse of energy, hence the name pulsars. These pulses are seen at very specific, predictable intervals, meaning that they can serve as excellent timekeepers.” When a gravitational wave passes between a pulsar and Earth, this alters the arrival time of the pulses. By carefully studying the accumulation of these timing “errors,” astronomers can infer the presence of the invisible gravitational waves.
The gravitational waves detected with PTAs are fundamentally different from those measured with LIGO. In the case of LIGO, astronomers are detecting signals received in the space of seconds or minutes. Meanwhile with PTAs, astronomers are looking for fluctuations in the spin periods of pulsars that occur over decades. “We have been monitoring these pulsars for roughly 15–20 years,” explains Sato-Polito. The main astrophysical source that produces gravitational waves of the frequencies detected by PTAs are supermassive black holes. Until 2023, when the first discovery of gravitational waves through PTAs was announced, the presence of supermassive black holes in our own galaxy and in nearby galaxies could be inferred by analyzing the gas or stars surrounding them, as well as through electromagnetic observations of the quasars, or jets, that the black holes eject, but with PTAs, the observations are more direct. Scholars can now measure the rates at which supermassive black holes are merging and can also learn more about the masses of the black holes involved.
In her work with Zaldarriaga and Quataert, Sato-Polito took the long-standing theoretical prediction for 1) what the population size of supermassive black holes ought to be, and 2) the expected number of different masses of those supermassive black holes, and compared it to the PTA data. “What we found is that the theory and the data were not incredibly consistent,” she says. “There are quite significantly more gravitational waves being detected than the theory currently predicts. To produce the gravitational wave background that we are currently seeing through PTAs, we would need ten times more supermassive black holes than the theory currently accounts for.”
Why is the theoretical picture so different from that gained through the data? In their initial paper, Sato-Polito, Zaldarriaga, and Quataert suggested that there might be a few particularly supermassive black holes out there that had not been previously measured, explaining the unexpected amount of gravitational waves in the data.5 But a subsequent analysis of the frequency patterns of gravitational waves detected by the PTAs has led to a different conclusion.6 “If the observed signals were produced by a small number of powerful sources, we would anticipate seeing significant statistical variations between the data captured at different frequencies,” explained Sato-Polito. “But such fluctuations were not present, so we now prefer a theory that there is a larger number of less massive black holes to explain the unexpected number of gravitational wave detections.” However, this answer is not definitive, and how precisely to resolve the discrepancies between the theory and the reality exposed by Sato-Polito, Zaldarriaga, and Quataert remains something of an open question. But this is precisely what excites Sato-Polito about this field of research. “One of the things that I find the most interesting about gravitational wave research is that it's a way of looking at the universe in a way that’s never been done before,” she says. “This result was something we were a bit surprised by, and the surprises are what intrigue me.”
How are merging black holes like a particle collider?
With their interest in subatomic phenomena, scholars working within the particle physics group typically investigate some of the smallest building blocks of our universe—which makes their contributions to the study of gravitational waves, which emanate from some of the most massive objects known to man, quite unexpected. Despite this, Members Holmfridur Hannesdottir, Sebastian Mizera (2019–24), and Simon Caron-Huot (2009–14), and their colleague Mathieu Giroux of McGill University, have identified some striking mathematical similarities between these fields in the form of “scattering amplitudes.”
As Hannesdottir explains, “at CERN’s Large Hadron Collider (LHC), we can measure what happens when two particles collide with each other: materials scatter off in different directions. Using the mathematical technique of scattering amplitudes, we describe what happens when those particles collide or interact, predicting the likelihood of different outcomes.” The new insight from Hannesdottir and her colleagues’ work is that the mathematical expression for the scattering amplitude of particles and the gravitational waveform are, in her words, “one and the same.”7 In short, they have demonstrated that the physics of gravitational wave emissions in black hole collisions can be understood by computing scattering amplitudes of particles. They have drawn these links by using complex analysis, namely the mathematical study of functions of so-called “complex numbers.”
Complex numbers combine both “real” and “imaginary” parts. A “real” number is a standard number such as 1, 2, 3, 4…that can describe the everyday world, but imaginary numbers are different in that, when squared, they give a negative result. The most basic imaginary number is i, defined as the square root of -1. Imaginary numbers (like i) do not directly correspond to measurable physical quantities but are an immensely useful mathematical tool. They can accurately describe quantum phenomena, namely the strange and counterintuitive behaviors that occur at the atomic and subatomic scales.8 Hannesdottir says that these complex numbers provide an “exact correspondence” between scattering amplitudes and gravitational wave signals.
Why is this significant? Mizera explains that these mathematical expressions make it possible to “quickly determine what kind of black holes or other heavy objects were present in the universe millions of years ago when these interactions took place, causing the gravitational waves that we see today,” providing an immensely useful time-saving tool.
How particle physicists can continue to contribute to the astrophysics community’s understanding of the universe in this way was highlighted in a panel at the Amplitudes 2024 conference, which brought more than 250 participants from across the globe to the Institute campus in June. “There used to be a language barrier between the two disciplines, but we're slowly learning to better communicate,” says Mizera. “Around the time of the first gravitational wave detection, it was like one side was speaking Spanish and the other Klingon, but now it's like Spanish and French!” Despite the differences in jargon, there is much to be gained from this boundary-crossing approach.
Hannesdottir adds, “Understanding the universe from Earth is hard! It's not like in a particle collider where we can measure almost everything that comes out of a collision. Instead, it's like we're in a basement where there is a tiny window to the universe, and we're trying to figure out everything about the universe from just the grass and flowers that we see from this window. Gravitational waves are an amazing new tool and they can measure things that we can't measure in any other way. So, gravitational wave research opens the basement window a little wider, and that is fascinating for those working in both areas of physics.”
The work of IAS scholars is opening windows, so to speak, in many areas, pushing the boundaries of our understanding of the cosmos. The Institute continues to be at the forefront of unraveling the mysteries of gravitational waves, a legacy extending from Einstein’s initial prediction all the way to today’s cutting-edge research.
[1] A neutron star is an extremely dense and compact stellar object formed from the collapsed core of a massive star after a supernova explosion.
[2] Each star population is characterized by its unique chemical composition.
[3] Rozner, M., and Perets, H. B. 2022. “Binary Evolution, Gravitational-wave Mergers, and Explosive Transients in Multiplepopulation Gas-enriched Globular Clusters.” https://doi.org/10.48550/arXiv.2203.01330
[4] The gas drains energy from black hole binaries both through its outflows or winds, which carry away material from the system, and through various torques and drag forces that extract angular momentum and rotational energy.
[5] Sato-Polito, G., Zaldarriaga, M., and Quataert, E. 2023. “Where are NANOGrav's big black holes?” https://doi.org/10.48550/arXiv.2312.06756
[6] Sato-Polito, G., and Zaldarriaga, M. 2024. “The distribution of the gravitational-wave background from supermassive black holes.” https://doi.org/10.48550/arXiv.2406.17010
[7] Caron-Huot, S., Giroux, M., Hannesdottir, H. S., and Mizera, S. 2023. “What can be measured asymptotically?” https://doi.org/10.48550/arXiv.2308.02125 and Caron-Huot, S., Giroux, M., Hannesdottir, H. S., and Mizera, S. 2023. “Crossing beyond scattering amplitudes.” https://doi.org/10.48550/arXiv.2310.12199
[8] An example of such a quantum phenomenon for which complex numbers are useful is superposition, where quantum objects can exist in multiple states at once until they are measured. This is famously illustrated by the Schrödinger’s cat thought experiment, where a cat is theoretically both alive and dead until observed.
