Neutrinos Skirting Black Holes Could Reveal the Universe’s Hidden Dark Matter

Neutrinos are the ghost particles of the cosmos: trillions of them pass through your body every second without leaving a trace, and they routinely cross entire galaxies unimpeded. But what happens when these elusive particles skim past a black hole wrapped in dark matter? A new theoretical study published in The European Physical Journal C suggests that the answer could open an entirely new window onto the dark sector of the universe, the mysterious components that make up roughly 95 percent of everything that exists. The research, led by Ikrom Ergashov and colleagues at New Uzbekistan University together with collaborators in Pakistan, Azerbaijan and China, calculates for the first time in detail how a black hole surrounded by dark matter in a phantom field background distorts the delicate quantum dance known as neutrino flavor oscillations.

Neutrino oscillations are one of the most remarkable phenomena in modern particle physics. Neutrinos come in three flavors, electron, muon and tau, but they do not travel as pure flavors. Instead, each flavor is a quantum superposition of three mass states, mixed together by the Pontecorvo-Maki-Nakagawa-Sakata matrix. As a neutrino races through space, these mass states accumulate slightly different quantum phases, and the relative phase difference determines the probability that the particle will be detected as a different flavor than the one it started as. The oscillation phase depends on the neutrino’s energy, the squared mass differences between the eigenstates, and the distance traveled. In flat spacetime the formula is elegant and well tested by experiments such as Super-Kamiokande, IceCube and Borexino. Curved spacetime, however, changes the game, because the phase must now be computed along the curved geodesic that the particle actually follows.

The team modeled a static, spherically symmetric Schwarzschild black hole immersed in what they call DMPF, dark matter within a phantom field background. This geometry, built from an Einstein-Hilbert action augmented with a scalar field, adds a logarithmic correction to the standard black hole metric, governed by a parameter a that encodes the density of the entire dark sector. The energy density of this dark component falls off as one over the cube of the distance from the hole, a profile consistent with the nearly flat rotation curves observed in spiral galaxies. By varying the dimensionless ratio a/M, where M is the black hole mass, the researchers could dial the strength of the dark matter influence up and down and watch how the neutrino oscillation patterns responded.

The first major result is a striking cancellation. For neutrinos traveling purely radially, straight outward from the black hole, the gravitational contributions to the oscillation phase exactly cancel. The phase difference between mass eigenstates ends up depending only on the radial distance, the mass-squared splitting and the neutrino energy, precisely as it would in flat spacetime. In other words, a neutrino beaming directly away from a black hole carries no memory of the gravitational maelstrom it just escaped, at least not in its oscillation phase. This result follows from expanding the covariant phase integral, built from the canonical momentum along the geodesic, in the ultra-relativistic limit where the neutrino mass is tiny compared with its energy, and it holds even in the presence of the dark matter logarithmic term.

The story changes dramatically for neutrinos whose paths are bent. When a trajectory is deflected by the gravitational field, characterized by a nonzero angular momentum and an impact parameter b, extra phase terms survive. The researchers derived analytical expressions showing that the dark matter parameter enters both as a small correction to the effective mass-splitting coefficient and as an additive logarithmic contribution to the total accumulated phase. When gravitational lensing splits the journey into two segments, from source to the point of closest approach and from there to the detector, the phase acquires further corrections involving the lens mass and the logarithm of the source and detector distances. Gravitational lensing thus does more than bend the neutrino’s path; it imprints measurable modifications on the interference pattern that determines which flavor arrives at the detector.

To make these abstract calculations concrete, the team computed two-flavor transition probabilities, electron to muon, for realistic astrophysical configurations. They considered three lensing objects: the Sun, Sagittarius A*, the four-million-solar-mass black hole at the center of our galaxy, and M87*, the 6.5-billion-solar-mass giant famously imaged by the Event Horizon Telescope. For Sagittarius A*, Event Horizon Telescope shadow observations constrain the dark sector parameter to values up to roughly 0.15 at two sigma, while for M87* the bound reaches about 0.33. The corresponding neutrino energies span an enormous range: solar neutrinos carry around 10 megaelectronvolts, astrophysical neutrinos detected by IceCube from sources such as the blazar TXS 0506+056 and the Seyfert galaxy NGC 1068 reach 10^8 to 10^10 megaelectronvolts, and hypothetical cosmogenic neutrinos, produced when ultra-high-energy cosmic rays collide with cosmic microwave background photons, could climb to the exaelectronvolt scale near M87*.

The numerical results reveal a rich structure. Plotting the transition probability as a function of the azimuthal angle of the source, the curves shift noticeably as the dark sector parameter is increased from zero, the pure Schwarzschild case, to a/M values of 0.05 and 0.1. The probability is highly sensitive to the dark sector density parameter, and it also depends on whether the neutrino mass hierarchy is normal or inverted. Intriguingly, the team uncovered a degeneracy: different combinations of lens mass and dark matter parameter can produce the same oscillation probability. For a fixed probability, achieving the same flavor transition under an inverted hierarchy requires a slightly larger a/M than under a normal hierarchy, and this difference grows with mass. This degeneracy is both a challenge and an opportunity, since breaking it with independent mass measurements could turn neutrino detectors into dark matter probes.

The study also tackled a subtler question: what happens when neutrinos are treated realistically as Gaussian wave packets rather than infinite plane waves? Wave packets of different mass states gradually separate in space, causing the oscillation pattern to wash out, a process called decoherence. Because gravity dilates proper time, neutrinos in curved spacetime must travel farther before their wave packets lose overlap. The researchers derived the effective damping factor for lensed trajectories and found that the dark matter background exerts only a minimal influence on decoherence. Instead, the absolute neutrino mass is the dominant factor determining the coherence length and the duration over which oscillations persist. Once decoherence sets in, the dark sector parameter has a negligible effect on the transition probability envelope, meaning that any dark matter signature must be extracted from neutrinos that are still coherent when detected.

The implications are tantalizing. In the Solar System, the dark matter density bound at one astronomical unit is so stringent that the parameter a/M is capped at roughly 7.5 times 10 to the minus 12, making dark matter effects on solar neutrino oscillations utterly unobservable with current techniques. But around supermassive black holes like Sagittarius A* and M87*, the allowed dark sector parameters are many orders of magnitude larger, and the extreme gravitational lensing amplifies the phase corrections. Future neutrino astronomy, whether through next-generation IceCube extensions, kilometer-cubic detectors in the Mediterranean, or hypothetical cosmogenic neutrino observatories, could in principle compare observed flavor ratios with the predictions of standard general relativity and detect the fingerprint of the dark halo surrounding these monsters.

Of course, this remains a theoretical edifice, resting on a two-flavor approximation and idealized geometries, and no one has yet observed a neutrino oscillation modified by dark matter. But the work demonstrates that the intersection of quantum interference and strong-field gravity is not merely a curiosity; it is a potential measurement channel. Any departure from the predictions of pure general relativity in neutrino flavor ratios arriving from the vicinity of compact objects would constitute compelling evidence for modified gravity or for the dark environments in which black holes are embedded. As detectors grow more sensitive and theoretical models more refined, the humble neutrino, the particle that barely interacts with anything, may become one of humanity’s sharpest tools for mapping the invisible universe that surrounds every black hole.

Subject of Research: Effects of dark matter in a phantom field background on neutrino flavor oscillations near black holes

Article Title: Probing dark matter and phantom field effects on neutrino oscillations around black holes

Article References: Ergashov, I., Narzilloev, B., Hussain, I., & Ahmedov, B. (2026). Probing dark matter and phantom field effects on neutrino oscillations around black holes. The European Physical Journal C, 86(9), Article 1032. https://doi.org/10.1140/epjc/s10052-026-16278-8

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16278-8

Keywords: neutrino oscillations, dark matter, black holes, phantom field, gravitational lensing, general relativity, neutrino astronomy, decoherence, Sagittarius A*, M87*, particle astrophysics, spacetime curvature