⚛️ phenomenology

High-Energy Neutrino Constraints on memory burdened Bardeen and Kerr Primordial Black Holes

This paper investigates how quantum memory burden effects, Bardeen regularization, and Kerr rotation influence the neutrino emission from primordial black holes, deriving constraints on their dark matter abundance using current and future high-energy neutrino observatories while highlighting the distinct impacts of spin and regularization on detection sensitivity.

Original authors: Md Riajul Haque, Suvashis Maity

Published 2026-08-24

📖 4 min read🧠 Deep dive

CC0 1.0

Original authors: Md Riajul Haque, Suvashis Maity

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast, cold darkness between the stars, a mysterious substance known as dark matter holds galaxies together, yet it remains invisible to our telescopes and undetectable by our instruments. For decades, scientists have searched for what this substance might be, with one intriguing possibility being that it consists of primordial black holes. These are not the massive black holes formed by collapsing stars, but rather tiny, ancient remnants created in the first fraction of a second after the Big Bang. According to standard physics, any black hole lighter than a specific weight—roughly the mass of a mountain—should have completely evaporated and vanished billions of years ago, leaving no trace today. However, a new line of thinking suggests that these tiny holes might not vanish so easily. If they carry a "memory burden," a quantum effect that slows down their evaporation, they could still be drifting through the universe today, potentially making up the dark matter we cannot see.

A team of researchers has now taken a closer look at how these memory-laden black holes would behave if they exist, specifically focusing on the particles they would emit. The study investigates two specific variations of these theoretical objects: one that is perfectly smooth and regular at its center, and another that spins rapidly like a top. By calculating how these different shapes and spins affect the release of high-energy neutrinos—ghostly particles that zip through the universe almost without interacting with anything—the scientists have mapped out exactly what we should be seeing if these black holes are real. They compared their predictions against data from some of the world's most sensitive neutrino detectors, including the massive IceCube observatory in Antarctica, to see if the universe is giving us any hints about their existence.

The researchers found that the shape and spin of these hypothetical black holes change the story significantly. For the smooth, regular black holes, the presence of a specific internal structure acts like a brake, lowering the temperature at which they emit particles. This cooling effect means they release fewer neutrinos than a standard black hole would, making them harder to detect. Consequently, the limits on how many of these objects could exist in the universe are looser; they could be more abundant without contradicting what we currently observe. In contrast, the rapidly spinning black holes tell a different tale. If a spinning black hole retains a significant amount of its rotation when it enters this slow-evaporation phase, it actually becomes a more potent source of neutrinos. The spin amplifies the emission, creating a brighter signal that allows scientists to place much stricter limits on their numbers. In this scenario, if such spinning black holes were common, we would likely have already seen their signature in our detectors.

The study also explored how the "memory burden" itself changes the game. This effect, which suppresses the rate at which black holes lose mass, allows lighter black holes to survive until the present day. As the suppression becomes stronger, the surviving black holes are not only lighter but also hotter, shifting the energy of the neutrinos they emit to much higher levels. This shift means that different experiments are needed to catch them. For weaker memory effects, current detectors like IceCube are already providing the tightest constraints. However, if the memory effect is strong, the signal moves to energies that future, even larger detectors will be required to see. The researchers highlight that upcoming facilities, such as the next generation of IceCube and a massive radio array called GRAND200k, will be crucial for probing these stronger suppression scenarios.

Ultimately, the work demonstrates that the geometry of a black hole and the quantum rules governing its memory are not just abstract details; they fundamentally alter what we can observe. The smooth, regular black holes hide more effectively, while the spinning ones stand out more boldly. By combining data from current observatories with the projected capabilities of future instruments, scientists can now carve out a much clearer picture of where these potential dark matter candidates might hide. The results show that while some versions of these memory-laden black holes could still be abundant enough to be dark matter, others are already ruled out by the silence of our detectors. As we build more sensitive eyes on the cosmos, we are closing in on the true nature of these ancient, invisible remnants, turning a theoretical possibility into a testable reality.

Technical Summary: High-Energy Neutrino Constraints on Memory Burdened Bardeen and Kerr Primordial Black Holes

Problem Statement
Primordial Black Holes (PBHs) are compelling dark matter (DM) candidates, yet standard semiclassical Hawking evaporation predicts that PBHs with masses $M \lesssim 10^{15}$ g would have evaporated by the present epoch, excluding them from contributing to the current DM abundance. However, the "memory burden" effect—a quantum backreaction arising from the unitary requirement that information remains encoded in the system—can suppress the evaporation rate once a PBH loses a significant fraction of its initial mass. This suppression allows lighter PBHs to survive until today. While previous studies have examined this effect for Schwarzschild PBHs, the interplay between memory burden, non-standard black hole geometries (specifically regular Bardeen black holes and rotating Kerr black holes), and high-energy neutrino observations remains unexplored. This paper addresses the need to constrain the abundance of such memory-burdened PBHs using current and projected neutrino data.

Methodology
The authors investigate the evaporation of PBHs described by two specific geometries: the regular, non-rotating Bardeen metric and the rotating Kerr metric, both subject to the memory burden effect.

Theoretical Framework: The mass-loss rate is modified by a suppression factor $S^{-k}$ (where $S$ is the Bekenstein-Hawking entropy and $k$ is the suppression index) once the PBH mass drops below a threshold $q M_{\text{in}}$ . The Bardeen geometry introduces a regularization parameter $l$ , while the Kerr geometry introduces a dimensionless spin parameter $\alpha_*$ .
Flux Calculation: The authors calculate primary and secondary neutrino emission spectra using the BlackHawk code and HDMSpectra for hadronization. They compute the total neutrino flux, summing contributions from the Galactic DM halo (using an NFW profile) and the isotropic extragalactic background.
Statistical Analysis: Constraints on the PBH abundance fraction $f_{\text{PBH}} \equiv \rho_{\text{PBH}}/\rho_{\text{DM}}$ are derived by comparing predicted fluxes against observational data. The analysis employs a background-agnostic likelihood function for existing data (IceCube HESE, Super-Kamiokande, ANTARES, and IceCube EHE) and projected sensitivities for future experiments (IceCube-Gen2, GRAND200k, and Hyper-Kamiokande), assuming zero observed events for future projections.

Key Contributions

Geometric Effects on Evaporation: The paper systematically quantifies how Bardeen regularization and Kerr rotation alter the neutrino flux in the presence of memory burden.
- Bardeen Regularization: Increasing the regularization parameter $l$ suppresses the Hawking temperature and the total evaporation rate, leading to a reduction in neutrino flux amplitude.
- Kerr Rotation: The effect of spin is conditional on the onset of the memory burden phase ( $q$ ). If the memory burden phase begins before significant spin-down (high $q$ ), a substantial residual spin remains. This enhances neutrino emission via rotational chemical potentials and spin-dependent greybody factors, resulting in stronger constraints compared to non-rotating cases.
Parameter Space Mapping: The study maps the surviving mass window of PBHs as a function of the memory burden parameters ( $k, q$ ) and geometric parameters ( $l, \alpha_*$ ), identifying regions where PBHs can survive to the present epoch.
Complementarity of Observatories: The work delineates the specific energy ranges and suppression regimes where different neutrino observatories provide the leading sensitivity.

Results

Bardeen PBHs: Increasing the Bardeen parameter $l$ weakens the constraints on $f_{\text{PBH}}$ . For $l=0.92$ , the limits are significantly looser than the Schwarzschild limit ( $l=0$ ) due to the suppression of the Hawking temperature and flux.
Kerr PBHs: Rapidly rotating PBHs with high initial spin ( $\alpha_{\text{in}}^* \approx 0.999$ ) and a high onset threshold ( $q=0.8$ ) exhibit enhanced neutrino emission. In these scenarios, the constraints on $f_{\text{PBH}}$ are substantially stronger than for non-rotating PBHs. Conversely, for lower $q$ (e.g., $0.5$), where significant spin-down occurs before the memory burden phase, the difference between spinning and non-spinning constraints diminishes.
Dependence on Suppression Index ( $k$ ): Increasing $k$ $k$ reduces the flux normalization but allows lighter, hotter PBHs to survive. This shifts the relevant signal to higher energies.
- For weak suppression ( $k=1$ ), the IceCube High-Energy Starting Events (HESE) provide the leading sensitivity.
- For stronger suppression ( $k=2, 3$ ), the signal shifts to higher energies, making IceCube-Gen2 and GRAND200k the most sensitive probes.
Current Limits: The paper presents 95% confidence level upper limits on $f_{\text{PBH}}$ across the surviving low-mass window, demonstrating that current data already excludes certain combinations of mass and abundance, while future experiments will probe deeper into the parameter space.

Significance
The paper demonstrates that the interplay between quantum memory effects and black hole geometry is critical for interpreting neutrino constraints on dark matter. It establishes that Bardeen regularization and Kerr rotation produce qualitatively different effects: regularization tends to weaken constraints by suppressing emission, while significant residual rotation can strengthen them by enhancing emission. The results highlight the complementarity of current (IceCube, Super-K, ANTARES) and future (IceCube-Gen2, GRAND200k, Hyper-K) neutrino observations in probing the existence and abundance of memory-burdened PBHs. By accounting for regular geometries and rotation, the study provides a more comprehensive framework for testing the PBH dark matter hypothesis against high-energy neutrino data.

Technical Summary: High-Energy Neutrino Constraints on Memory Burdened Bardeen and Kerr Primordial Black Holes

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