Black Hole Mergers Show Strange Mathematical Link to String Theory

Yahoo

15-05-2025

A decade ago astrophysicists at the Laser Interferometer Gravitational-Wave Observatory (LIGO), operated by the California Institute of Technology and the Massachusetts Institute of Technology, managed to detect subtle ripples in spacetime called gravitational waves, released by a pair of black holes spiraling into each other, for the first time. That impressive discovery—which earned the 2017 Nobel Prize in Physics—has since become commonplace, with researchers regularly detecting gravitational waves from myriad far-distant celestial sources.
And as the numbers of gravitational-wave observations have increased, physicists' careful modeling is revealing new details about their mysterious origins. Some of the most intriguing gravitational-wave events, it turns out, could arise not from catastrophic collisions but rather from near misses. Furthermore, these cosmic close calls might be best understood using concepts derived from string theory—a notional theory of everything that posits that all of nature is fundamentally composed of countless, wriggling subatomic strings. This arguably marks the first linkage to date between a core mathematical aspect of the arcane theory and real-world astrophysics.
At least, that's the conclusion of an international team of researchers that applied geometric structures inspired by particle physics and string theory to the behavior of black holes when the colossal objects closely pass and deflect each other. Such interactions between black holes or neutron stars (compact remnants of exploded massive stars) can be studied through the deflection angle, the energy released through the near miss and the momentum of the objects' recoil—all of which may be discerned in gravitational waves. The team's results were published in the journal Nature on Wednesday.
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In their study, the researchers used an obscure class of abstract mathematical functions to solve the formidable equations involved in determining the radiated energy from a near miss. 'You need these new functions, which, in math and mathematical physics, have been studied intensively but, to date, have not appeared in any real physical observable. That's what makes it quite interesting,' says Jan Plefka, a theoretical physicist at the Humboldt University of Berlin and a co-author of the new study. Those obscure functions, known as six-dimensional Calabi-Yau manifolds, had never been shown as directly relevant to descriptions of real astrophysical phenomena before.
In the years since LIGO's initial detection, two additional major gravitational-wave observatories, Europe's Virgo and Japan's Kamioka Gravitational-Wave Detector (KAGRA), have come online. Together, they form the international LIGO-Virgo-KAGRA collaboration and have amassed detections of nearly 300 gravitational-wave events over the past decade, mostly from colliding pairs of black holes. Also called black hole 'mergers,' such events are the cacophonous moment when these dense gravitational behemoths smash together to form a single, larger beast. Plefka and his colleagues are studying different interactions known as 'scattering' events, which occur when paired black holes slip by each other, usually in prelude to their eventual coalescence. During these close encounters, the clashing gravity of the black holes causes each to accelerate past the other, generating a significant gravitational-wave signal, but the objects are sufficiently separated to avoid merging.
It's no coincidence that this resembles elementary particles deflecting each other. 'You can use the techniques developed for the scattering of microscopic objects to describe this scattering of macroscopic ones,' Plefka says. Considered from far enough away, well beyond the event horizon—that pivotal region within which neither matter nor light can escape—a black hole can be modeled as a particlelike point with mass and spin, albeit one that generates gravitational rather than electromagnetic waves.
On that basis, Plefka and his colleagues applied techniques from quantum field theory that are more typically used to analyze the behavior of elementary particles. 'We're building on decades of work that has been done to make predictions for collider experiments,' says Gustav Mogull, a particle physicist at Queen Mary University of London and one of Plefka's co-authors.
The team's goal was to bring its numerical approximations as close as possible to mirroring reality—which, of course, tends to be more messy. To do that, Mogull, Plefka and their team toiled to crank up the complexity of their calculations. In this work, the researchers incorporated five levels of that complexity—to what is known as the fifth post-Minkowskian order of precision—for describing the scattering angles of black hole pairs, their radiated energies and their recoils.
This is where the Calabi-Yau geometric structures, normally associated with string theory, come in. In string theory, Calabi-Yau geometries involve the compactification of higher dimensions. Here, they are not merely abstractions but instead emerge from the researchers' calculations of black hole scattering. It's perhaps ironic that string theory, notoriously derided as untestable, has given rise to mathematical structures of relevance to measurable physics far from the rarefied realm of strings.
Any mathematical function is associated with some kind of geometry, Mogull explains—and as the function increases in complexity, so, too, does its geometry. In the case of something basic, such as the sine or cosine functions used in trigonometry, that geometry is a simple circle. Elliptic functions, on the other hand, imply a doughnut-shaped geometry called a torus, which is also a Calabi-Yau onefold. It turns out that the functions Mogull, Plefka and their team developed for black hole scattering are associated with Calabi-Yau threefold structures, which involve six-dimensional surfaces. 'I don't think the appearance of Calabi-Yaus was that unexpected within our community. I would say this represents confirmation of something that people had suspected but was yet to be verified,' Mogull says.
To demonstrate the utility of their approach in their study, Plefka, Mogull and their colleagues compare their approximations of black hole scattering angles to other, presumably more precise ones that were derived from numerical simulations. Such simulations can be time-consuming to run, even on state-of-the-art supercomputers—hence the search for accurate approximations. The team's highest-order approximation closely matches the results of supercomputer number crunching for cases of black holes that gently deflect each other across great distances. But when the black holes come closer to a head-on collision, the team's calculations begin diverging from the numerical simulations.
Such work may seem to be a purely academic exercise, but in fact, the research could prove vital for making new discoveries. Signals from scattering black holes and neutron stars should be within reach of the next generation of gravitational-wave detectors that are set to come online in the late 2030s. These detectors, which will also need a new generation of models called waveform templates to discern true gravitational-wave signals from a sea of cosmic and terrestrial noise, include the proposed Einstein Telescope in Europe and Cosmic Explorer in the U.S. The latter, like LIGO, is supported by the National Science Foundation, and so far these kinds of gravitational-wave projects have avoided being directly targeted by the Trump administration's aggressive proposed cuts to federally funded science.
The work's prospect for enhancing our understanding of gravitational-wave sources excites scientists who are gearing up for this new wave of detectors. They include Jocelyn Read, a physicist at California State University, Fullerton, who works with the Cosmic Explorer project. 'Next-generation facilities can measure nearby signals with exquisite fidelity,' she says. (Here 'nearby' means 'within a few billion light-years.') 'So having very accurate and precise predictions from our current theories is definitely needed to test them against those kinds of future observations,' Read adds.
Yet she also urges caution when assessing the significance of Plefka, Mogull and their colleagues' work. 'If they're talking about implications for gravitational-wave astronomy, there are a few more steps that are needed,' she says. And their team has competitors, too, including some who have been deploying numerical simulations of their own.
These kinds of approximate methods could eventually inform the waveform templates that are so crucial for filtering out noise in upcoming gravitational-wave detectors, Plefka says. Geraint Pratten, a LIGO physicist at the University of Birmingham in England, agrees. 'I think it's a heroic calculation by the group. It will provide a lot of insight into how we can structure next-generation waveform models,' he says. Pratten adds that more work will need to be done to move past the new study's limitations. For example, the paper focuses on black holes without spin and those that undergo 'unbound' scattering, which means that they deflect each other and never meet again. In reality, most, if not all, black holes are thought to spin, and usually scattering events precede an eventual merger.
But in any case, he believes some gravitational waves from black hole and neutron star deflections will eventually be detectable, such as through observations of globular clusters, where these dense objects are packed together in a small space, cosmically speaking.
For Plefka, Mogull and their peers, this macroscopic version of quantum field theory is still a young field, and there are many new types of astrophysically relevant calculations that they and others can do. These esoteric Calabi-Yau structures, formerly on the frontier of theoretical physics, could be just the beginning. 'You've had this whole new class of mathematical functions—these theoretical things that had appeared in string theory,' Mogull says. 'And we're saying, 'Look, this is tangible. This [radiated energy from scattering] is something you can try to detect, try to measure. This is real physics now.''