At the centre of our galaxy lies a supermassive black hole, Sagittarius A* (Sgr A*), that’s more than four million times the mass of the Sun. Astronomers have now discovered the fastest-known star in the Milky Way zooming around this black hole in an extremely close orbit. Observations of this star, known as S301, could shed new light on the spin of Sgr A*.

Black holes are extremely large concentrations of matter condensed into very small regions of space. As a black hole spins, it drags the surrounding space–time around it, a phenomenon known as frame dragging or the Lense-Thirring effect. This frame dragging creates a cosmic whirlpool, twisting the fabric of space–time and warping the orbits of nearby stars. However, unless the orbiting star reaches very close proximity, this subtle effect is difficult to measure.

“Our group has determined the mass of the central black hole down to sub-percent precision,” says team member Felix Mang, a PhD student at Max Planck Institute for Extraterrestrial Physics (MPE) and author of the study published in Nature. “A black hole is characterized exclusively by its mass, spin, or angular momentum and electric charge; now that we’ve measured the mass really, really accurately, the next step is to measure the spin.”

Probing Sgr A*

Astronomers can measure black hole spin through various methods, including X-ray reflection spectra and the thermal X-ray emission of the gas disk surrounding stellar-mass black holes, as well as gravitational-wave signatures from merging black hole binaries.

Lying in the galactic centre approximately 27,000 light-years from Earth, Sgr A* offers another direct way to measure its spin. There are a few dozen stars whirling around the massive black hole on nearly Keplerian orbits. The stars that come closest to Sgr A* most effectively probe its spin as they reach into the deepest parts of the gravitational potential, altering their trajectories.

For example, the star S2 is on a 16-year orbit and has been meticulously tracked using the GRAVITY instrument on the European Southern Observatory’s Very Large Telescope Interferometer. GRAVITY’s emergent near-infrared interferometry enabled the detection of strong relativistic effects during S2’s close approach in 2018, including a 12-arcminute orbital precession consistent with the Schwarzschild metric derived from Einstein’s general theory of relativity.

Despite these measurable relativistic effects, even at its pericentre when it is closest to Sgr A*, S2 remains too far away to detect the black hole’s spin without prohibitively long years of observation.

Discovery of S301

Although S2 is not a suitable candidate for Sgr A* spin measurements, the newly discovered star S301 is an ideal cosmic probe. Mang notes that the star is “a bit heavier than the Sun, and it has a radius which is a bit bigger; but overall, it’s not that special”. S301 is under 1.5 solar masses with a radius about 1.4 to 1.6 times that of the Sun, and it is too faint to be one of the giant stars in the galactic centre. Although the main-sequence star S301 may seem fairly ordinary, its extremely eccentric orbit and very close approach to the supermassive black hole are remarkable.

“We found the star in Spring 2023,” recalls Mang. Upon detection, the team could not conclude whether it was a foreground or a background star. However, dedicated follow-up observations in 2024 revealed a pronounced acceleration in S301’s proper motion, or apparent angular change of position on the sky. “It was curving away from a linear trajectory, which gave us a hint that it may be bound to the black hole,” Mang explains. Continued observations in 2025 allowed the team to create a robust initial model of S301’s orbit, revealing it to be “indeed a very eccentric and tightly orbiting star, which was then later on confirmed”.

Armed with evidence that the star might be gravitationally bound to Sgr A*, the team looked to the past, hoping to lock down S301’s orbit. Combing through archival data, the astronomers searched for traces of the star before its close approach in 2023. As Mang notes, “getting these two pre-peri positions in 2021 and 2017 was rather challenging, [we were] digging through the data”. The meticulous hunting paid off and revealed a strong trace of S301 in 2021 and a weaker signature back in 2017.

With 19 distinct positions found across nearly a decade of data, the team outlined a clear elliptical orbit, revealing that the star had zoomed past the supermassive black hole at its closest approach in early 2023 and passed significantly closer to the black hole than S2 ever has.

Extreme path of S301

The team determined that S301 boasts an orbital period of just 8.7 years, making it the shortest known orbital period around Sgr A*. This breaks the previous record, held by the star S55, which takes about 12 years to complete its path.

But S301’s orbital period is only part of what makes its path extraordinary. With an eccentricity of about 0.98, S301’s elongated path brings the star to a pericentre distance of approximately 1.78 billion kilometres, roughly 10 times smaller than that of S2. At that closest approach, S301 speeds around at about 25,000 km/s, making it the fastest known star in the Milky Way.

Because S301 gets so close to the supermassive black hole, general relativity strongly affects its orbit. In particular, S301 experiences a phenomenon known as the Schwarzschild precession, which shifts the star’s orbit by about 2° per revolution. Over the course of roughly 1500–1600 years, those slight shifts accumulate into a full 360° rotation of the orbit.

While this dramatic shift is driven by the colossal mass of Sgr A*, S301’s extreme orbit is also subjected to a subtler spin-induced effect: the Lense-Thirring precession. As Sgr A* spins, the twisted space–time forces S301’s orbital plane to slowly wobble, making it a powerful probe of the curved space–time around Sgr A*. By precisely tracking the star’s motion, astronomers can examine how its trajectory is shifted by these two precession effects, thereby enabling them to measure the spin of the supermassive black hole.

Looking forward, the upcoming years should bring substantially better data. “The instrument we are observing with, GRAVITY, has undergone some major upgrades, which gives us more flux, and we also expect to get better astrometric precision,” Mang says. “Along with that, we expect the Extremely Large Telescope, and one of its first light instruments, MICADO, to be operational by roughly 2030.”

These advances will allow astronomers to trace the motion of S301 with incredible precision. As a result, the team is confident that these instruments will decode the mystery of Sgr A*’s spin. “Combining the astrometry or proper motion measured with GRAVITY on the sky of that star, and then having a perception of the velocity of that star in the plane or out of the plane of the sky with MICADO, will allow the measurement of SgrA*’s spin, probably within the next 10 years,” Mang explains.

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Usually, when physicists want to model the merger of two black holes, they use supercomputers. Now, however, physicists in the US have found a possible shortcut. In a study published in Physical Review Letters, they show that, of the final states permitted by energy and angular momentum, the remnant of a non-spinning black hole merger ends up in a state quite close to one that maximizes the system’s entropy – a surprising and puzzling result that reinforces the deep connection between thermodynamics and black holes.

“Our group has long believed that black hole thermodynamics could provide a new perspective on binary black hole mergers,” says team member Monica Rincon-Ramirez, a postdoctoral researcher at Pennsylvania State University. “While black hole thermodynamics is well established for equilibrium systems, much less is understood in the highly dynamical regime of mergers.”

Merging black holes

Black hole mergers occur when two black holes that orbit each other spiral inward with increasing speed, losing both energy and angular momentum by emitting gravitational waves until they eventually converge in a violent clash. After the moment of merger, the remnant oscillates vigorously, “ringing down” into a quiescent, rotating object known as a Kerr black hole that can be described in terms of just two quantities: mass and spin.

Meanwhile, the gravitational waves – ripples in the fabric of spacetime – from this energetic collision propagate through space virtually uninterrupted. These gravitational waves encode information about their source, and when we detect them on Earth (millions of light-years away from their origin), we can use them to predict the remnant’s size and spin. However, doing this requires solving complex equations from Einstein’s general theory of relativity using computationally expensive numerical simulations.

Connecting black holes and thermodynamics

Thermodynamics is the branch of physics concerned with the relationships between energy, heat, work and temperature. For ordinary matter, thermodynamics can describe how energy flows from one system to another in simple terms, even for complex systems with numerous particles and degrees of freedom. For example, rather than meticulously tracking each individual particle, concepts such as entropy – a measure of a system’s disorder – can be used to describe the final state of the entire system.

Physicists have long known that black holes obey laws that closely parallel the laws of thermodynamics, with the event horizon and surface gravity of black holes being analogous to entropy and temperature, respectively. Building on this established connection, Rincon-Ramirez and colleagues at the University of Mississippi, the University of California, Berkeley, and Northwestern University as well as Penn State investigated whether black hole thermodynamics could go beyond describing the properties of isolated, stationary black holes and provide, in addition, a principle for determining the final state of a merger.

The maximum-entropy conjecture

After accounting for the energy and angular momentum carried away by gravitational waves, the researchers tracked the evolving mass and angular momentum of a binary, mapped these values to those of hypothetical Kerr black holes, and calculated the corresponding entropy. They found that the Kerr entropy reaches a maximum at a mass and spin strikingly close to the final mass and spin predicted by numerical relativity simulations. Indeed, the two methods agreed with each other to within a few percent. “The Kerr entropy turned out to be remarkably meaningful for the binary system as a whole,” Rincon-Ramirez says.

Interpreting and presenting these results proved to be a challenge, however. “What we found was completely unexpected,” says Rincon-Ramirez. After deliberating among themselves as to why the final black hole’s parameters should lie so close to those of the maximum-entropy black hole, they ultimately chose to extend the conversation to the scientific community. By presenting their puzzling results and a broad conjecture, which they term the “maximum entropy conjecture for black hole mergers”, they hope to sharpen their findings through rigorous testing and eventually place them on a firm mathematical foundation within general relativity.

In the meantime, the researchers plan to extend their conjecture to more general binary black hole systems. By studying systems such as highly spinning and eccentric binaries, they hope to gain further understanding of the role of thermodynamic quantities in general relativity. “Ultimately, we hope this work will contribute to a more complete thermodynamic framework for highly dynamical spacetimes,” Rincon-Ramirez says.

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Physicists have developed a model that predicts how gravitational-wave emission changes when a binary black hole system moves through dark matter. Gravitational waves are ripples in spacetime generated by compact objects spiralling together in a cosmic dance that ends in a violent collision. In the presence of dark matter, these waves may carry an imprint of the surrounding environment. Despite making up over 80% of all matter, dark matter does not interact with the electromagnetic force, and its existence has been surmised only by its gravitational interactions, leaving its precise nature a mystery. Gravitational waves may provide a new way to probe the characteristics of dark matter.

One proposed dark-matter candidate is the light scalar boson, an extremely small particle orders of magnitude lighter than an electron, that can exhibit coherent wave-like behaviour. In the presence of spinning black holes, a process called superradiance can transfer rotational energy into the surrounding field of ultralight boson particles, amplifying the dark matter into a dense cloud around the black hole. These clouds can modify the dynamics of black hole binaries, encoding observable signatures into the gravitational-wave signals that they emit.

To understand what these signatures may look like, an international team of researchers developed a model for gravitational-wave emission from a binary black hole system moving through dark matter. Developing their model required meticulous numerical relativity simulations, but ensuring their results were accurate and reliable proved to be a challenge.

“The hardest part was making sure we truly understood what the simulations were telling us. The danger in numerics is fooling yourself,” explains Josu Aurrekoetxea of Massachusetts Institute of Technology. “You run a simulation, you see an effect, and you have to ask – is that dark matter, or is that my code?”

Working with Katy Clough of Queen Mary University of London and Pedro Ferreira of the University of Oxford, Aurrekoetxea spent several years developing these simulations, before joining forces with Soumen Roy of Université Catholique de Louvain and Rodrigo Vicente of the University of Amsterdam, whose expertise in analytical modelling and data analysis helped the team construct and validate the novel waveform model.

Most work in the field of gravitational waves and dark matter focuses on observations with future space-based detectors such as the Laser Interferometer Space Antenna. “Our motivation was to ask what could already be learned about specific dark-matter models using the LVK [LIGO–Virgo–KAGRA] gravitational-wave data available today,” says Vicente. “We were surprised to find that some of the more extreme models can already begin to be tested with signals observed by current experiments.”

Searching for these dark-matter imprints, they applied their model to 28 publicly available signals observed by the LVK collaboration, a global gravitational-wave detector network that has observed signals from hundreds of mergers. For each event, the team compared the signal to their predictive dark matter-modulated waveform and the standard waveform for black holes merging in a vacuum.

After rigorous testing, the researchers found that 27 of the 28 events were consistent with gravitational-wave signals expected from binary black holes evolving in empty space. One event, GW190728, showed a slight preference for the dark-matter model, indicating that its signal contains properties consistent with modulations from the presence of dark matter. However, the statistical evidence is not strong enough to claim a confident detection of a dark-matter imprint.

Although only one event demonstrated a preference for the predictive dark-matter model and no definitive claim of a dark-matter signature could be made, the researchers have demonstrated a novel method to probe and characterize dark matter through signatures encoded in gravitational-wave signals.

“Our findings from GW190728 suggest that, if this interpretation is correct and we are seeing a genuine environmental signature, similar effects may appear in future LVK events,” says Roy. Therefore, the next step for the researchers is to extend their analysis to LVK’s fourth observing run. Roy also says that if they can estimate the number and types of events that should carry dark-matter imprints, they can combine multiple signals to test their hypothesis more robustly.

“It has become clear that gravitational waves have tremendous potential to help us understand how matter behaves in the extreme gravitational fields surrounding black holes. This is particularly relevant for dark matter, which may interact only through gravity,” says Vicente. And as more gravitational-wave signals are observed, they provide a promising channel to uncover the elusive nature of dark matter.

The research is described in Physical Review Letters.

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