Philip Hampsheir, with Claude (Anthropic)

First published 24th April, 2026

Abstract

We propose that the cosmic neutrino background (CνB) — the relic neutrino field permeating the universe at approximately 336 particles per cubic centimetre — accumulates gravitationally around black holes through cosmological clustering in galactic potential wells, producing an enhanced relic neutrino density at black-hole-scale radii. Because neutrinos possess nonzero mass and travel at subluminal velocities, the three mass eigenstates cluster with different spatial distributions — heavier eigenstates concentrate more tightly due to their lower velocities — creating a gravitationally stratified shell structure around every galactic black hole in the universe, a structure we term the neutrino onion. A critical and potentially the most distinctive feature of this structure is oscillation-driven shell churning: bound neutrinos are quantum mechanically delocalised across all three eigenstate shell radii simultaneously, with their wave packets continuously breathing across the shell structure at frequencies set by neutrino mass splittings and local spacetime geometry — a quantum-gravitational phenomenon with no classical analogue. Conservation of energy demands that as captured neutrinos undergo orbital decay toward the innermost stable circular orbit (ISCO), energy must be radiated away. We identify several conventional radiation mechanisms and their associated observational signatures, ranked by detectability with current and near-future instruments. We note that the Majorana versus Dirac nature of the neutrino produces quantitatively distinct predictions for the annihilation channel, potentially offering a novel discriminant for this long-standing open question. A separate section, to be developed, addresses quantum field theoretic effects in strongly curved spacetime, including Unruh radiation contributions from the orbital acceleration of shell neutrinos. The full framework connects established particle physics (neutrino mass, CνB, oscillations) with general relativistic orbital mechanics and standard astrophysical observables, requiring no new physics beyond what is already confirmed. Several predicted signatures are at or near the threshold of current observational capabilities.

1. Introduction

Black holes are conventionally treated as passive gravitational sinks in discussions of the cosmic neutrino background. The CνB — a relic thermal bath of neutrinos and antineutrinos decoupled approximately one second after the Big Bang, now cooled to roughly 1.95 K — permeates the universe uniformly at ~336 cm⁻³ (combined flavours and helicities). While the gravitational clustering of relic neutrinos around large-scale structure has been discussed in the context of cosmological neutrino mass constraints (e.g., overdensity around galaxy clusters), the specific question of long-term gravitational capture and stratified accumulation around individual black holes over cosmological timescales has not, to our knowledge, been quantitatively addressed as a source of conventional astrophysical observables.

The argument for considering this problem seriously rests on three pillars:

First, neutrinos have mass. The oscillation experiments beginning with Super-Kamiokande (1998) and the Sudbury Neutrino Observatory established beyond doubt that the three neutrino mass eigenstates (m₁, m₂, m₃) are nonzero and distinct. The mass-squared splittings are measured: Δm²₂₁ ≈ 7.5 × 10⁻⁵ eV² and |Δm²₃₁| ≈ 2.5 × 10⁻³ eV². Absolute masses remain poorly constrained but are bounded by cosmological observations to Σm_ν < 0.12 eV. The critical point is that any nonzero mass means neutrinos travel at subluminal velocity and follow timelike rather than null geodesics in curved spacetime.

Second, black holes are long-lived. Stellar-mass black holes persist for timescales vastly exceeding the current age of the universe before Hawking evaporation becomes relevant. Supermassive black holes (SMBHs) are similarly ancient, with Sgr A* having accreted to its current mass of ~4.3 × 10⁶ M☉ over billions of years. This provides enormous integration time for gravitational capture processes that would be negligible on short timescales.

Third, conservation of energy is non-negotiable. Any neutrino captured into an orbit around a black hole that subsequently decays inward must radiate away the energy difference between its initial and final orbital states. The question is not whether this radiation occurs but what form it takes and whether it is detectable.

The present paper develops this framework, identifies the observable signatures, discusses detectability against known astrophysical backgrounds, and highlights two particularly novel aspects: the mass eigenstate stratification as a natural neutrino mass spectrometer, and the Majorana-versus-Dirac discriminant encoded in the annihilation channel luminosity.

2. The Cosmic Neutrino Background and Gravitational Capture

2.1 CνB Properties Relevant to Accumulation

The CνB neutrinos relevant to this discussion have characteristic energies of order k_BT_ν ≈ 1.7 × 10⁻⁴ eV. Given that neutrino masses are of order 0.01–0.1 eV, the relic population is either mildly relativistic or non-relativistic today, depending on the exact mass values. Non-relativistic or mildly relativistic particles are far more susceptible to gravitational clustering than ultra-relativistic ones, because their velocities are lower and gravitational effects act over longer timescales.

A critical point of physical honesty must be stated at the outset: in a pure vacuum two-body system, a neutrino on a hyperbolic fly-by trajectory past a black hole remains on a hyperbolic trajectory after the encounter. Gravitational focusing deflects the particle; it does not bind it. True capture into a bound orbit requires either energy dissipation, a three-body interaction, or — and this is the correct mechanism — cosmological binding during structure formation.

Relic neutrino accumulation in gravitational potential wells is established physics, not speculation. Ringwald and Wong (2004, Phys. Rev. D 72, 103503) and subsequent work — including Zhang and Zhang and Mertsch et al. on local CνB overdensity — have computed CνB overdensities around galactic potentials of factors of roughly 10 to 20 for heavier mass eigenstates, with the enhancement rising further in cluster potentials. The mechanism is cosmological: as large-scale structure formed, growing potential wells captured the slow tail of the CνB velocity distribution through violent relaxation and adiabatic deepening of the potential. Relic neutrinos are genuinely gravitationally bound inside galaxies today. The black hole at the centre of a galaxy does not individually accrete its own neutrino population — it sits inside a much larger pre-existing bound relic neutrino cloud whose density profile is set by galactic-scale dynamics. The BH provides the deepest point of that potential well, concentrating the already-bound neutrino overdensity most strongly at its centre.

This reframing is more modest than per-BH sweep-up accumulation, but it is stronger for being defensible. The neutrino onion described in Section 3 is a galactic onion with the black hole at its centre, not a black-hole-generated one. Critically, the Ringwald-Wong result already encodes the mass-eigenstate stratification we describe: heavier mass eigenstates have lower velocities at fixed momentum, cluster more tightly in gravitational potentials, and are therefore more concentrated toward the galactic centre and the central black hole. The stratification is real; it emerges from established cosmological physics.

2.2 Orbital Dynamics of the Bound Relic Population

Given a pre-existing bound relic neutrino population in the galactic potential, the central black hole imposes its own gravitational structure on the innermost portion of that population. Neutrinos from the cosmologically bound halo that pass within the region dominated by the black hole’s gravity — the sphere of influence, where the BH’s gravitational pull exceeds the galactic potential — follow geodesics in the Schwarzschild or Kerr metric rather than the galactic potential.

Within this region, the different mass eigenstates occupy different orbital radius distributions, as their different masses translate to different velocity distributions at fixed momentum (from the common decoupling epoch), and therefore different specific angular momenta. The natural result is a density profile stratified by mass eigenstate — the neutrino onion — whose structure is set by the interplay of the galactic overdensity profile and the BH’s central potential.

Honesty about the diluteness of the accumulated shell population is essential to the credibility of this framework. For Sgr A* (M ≈ 4.3 × 10⁶ M☉), the relic neutrino density at BH-scale radii is enhanced above the cosmic mean by galactic clustering factors, but the total mass in neutrinos near the black hole remains a tiny fraction — roughly 10⁻¹⁰ to 10⁻¹² of the black hole mass, possibly less. The argument for detectability therefore does not rest on the halo being massive, but on three compounding factors: cosmic accumulation timescales (10¹⁰ years), the inescapable geometry (every infalling particle crosses the shells), and the extraordinary precision of current and forthcoming instruments. The effects are genuinely small; the instruments are genuinely extraordinary.

3. The Neutrino Onion: Mass-Eigenstate Shell Stratification

3.1 The Basic Stratification Argument

The orbital radius of a massive particle in a circular geodesic around a Schwarzschild black hole depends on the particle’s mass and energy. For CνB neutrinos arriving with similar kinetic energies, the three mass eigenstates (m₁ < m₂ < m₃ in normal hierarchy, or m₃ < m₁ < m₂ in inverted hierarchy) will, over time, populate orbital shells at slightly different radii.

The physical intuition is clean: a heavier particle at the same total energy has more of its energy tied up in rest mass and less available as kinetic energy. The relationship between orbital radius and the ratio of kinetic to rest-mass energy in the Schwarzschild metric means that particles with different masses but similar total energies settle into slightly different preferred orbital bands. Over billions of years of continuous infall and redistribution, this produces a gravitationally sorted population — the neutrino onion.

The radial separation between eigenstate shells is small in absolute terms — the mass splittings are tiny fractions of the neutrino energy — but the separation is systematic and cumulative. Every black hole in the universe is, in this sense, acting as a neutrino mass spectrometer, with the radial coordinate encoding the mass eigenstate. If the radial structure of the neutrino halo could be read out, it would provide a measurement of absolute neutrino masses (not merely mass-squared differences) encoded in the shell spacing.

3.2 Oscillation-Driven Shell Churning: The Distinctive Signature

The stratification described above would, if static, be difficult to distinguish observationally from any other form of distributed dark mass around a black hole. What makes the neutrino onion distinctive — and in principle falsifiable rather than merely plausible — is the dynamic character imposed by neutrino oscillations.

Neutrino mass and flavour eigenstates are not the same: a neutrino produced as an electron neutrino is a quantum superposition of mass eigenstates m₁, m₂, m₃. During propagation, the phase relationship between these components evolves, causing the neutrino to oscillate through electron, muon, and tau flavour states with a characteristic vacuum oscillation length L_osc ∝ E/Δm².

Running the numbers for CνB energies: for E ≈ 1.7 × 10⁻⁴ eV and Δm²₂₁ ≈ 7.5 × 10⁻⁵ eV², the vacuum oscillation length is L_osc ≈ 5–6 micrometres. The ISCO circumference for a 10 M☉ stellar-mass black hole is hundreds of kilometres; for Sgr A* it is approximately 2.4 × 10¹¹ metres. Both are larger than L_osc by eleven and sixteen orders of magnitude respectively. Every astrophysical black hole is therefore deep in the oscillation-churning regime — the qualitative distinction between stellar-mass and supermassive black holes that an earlier version of this framework proposed does not survive the arithmetic. We state this explicitly: the churning is universal across all black hole masses on these numbers, and the specific falsifiable frequency fingerprint based on that distinction is withdrawn.

There is an additional subtlety worth acknowledging: the standard L_osc formula is derived under the ultra-relativistic approximation. For CνB neutrinos that may be non-relativistic or mildly relativistic today, this formula does not apply cleanly. The oscillation treatment for non-relativistic neutrinos involves wave-packet coherence arguments that are genuinely unsettled in the literature and do not straightforwardly reduce to a single length scale. This is an open theoretical problem that any future quantitative development of this framework must confront.

What survives this correction is the wave-packet picture, which is independent of the specific churning frequency. A question of physical interpretation: is the radial displacement of an oscillating neutrino modelled as a series of classical orbital kicks, or as a delocalised quantum wave packet simultaneously occupying all three eigenstate shell radii? The correct answer is the latter. A neutrino in orbital motion is not classically ‘in’ one shell. It is a quantum superposition of mass eigenstates, each with its own preferred orbital radius, and therefore quantum mechanically delocalised across the full onion thickness. The neutrino collapses to a specific eigenstate shell only upon interaction. The churning, on this view, is a continuous oscillatory breathing of the wave packet across the shell structure — a quantum-gravitational phenomenon with no classical analogue. This picture is elegant and worth developing further as a thought experiment about a single bound neutrino in the Schwarzschild metric, independent of the full accumulation story.

3.3 The Sterile Neutrino Case

If sterile neutrinos exist — a fourth flavour that couples only gravitationally and not through the weak force — they would be captured into orbital shells with even greater efficiency than active flavours, as nothing deflects them except gravity and they cannot escape via any weak interaction channel. The sterile neutrino shells, if present, would contribute additional gravitational mass to the halo at radii determined by the sterile mass eigenstate. An anomalously large halo mass fraction, compared to predictions from active flavours alone, would be an indirect signature of sterile neutrinos.

4. Orbital Decay Radiation: What Must Come Out

This section addresses the ironclad conservation argument. A neutrino in an orbital state outside the ISCO carries a specific orbital energy E_orb relative to a neutrino at the ISCO. As radiation losses carry away angular momentum and energy, the orbit decays inward. The total energy radiated between any initial orbital radius r_i and the ISCO is:

ΔE = E_orb(r_i) – E_orb(r_ISCO)

This energy must go somewhere. The candidates are:

4.1 Gravitational Wave Emission

Any mass following a curved path in spacetime emits gravitational radiation. For a single neutrino of mass m_ν in orbit around a black hole of mass M, the emitted gravitational wave power is:

P_GW ∝ G⁴ m_ν² M³ / (c⁵ r⁵)

For a single neutrino, this power is fantastically small — the neutrino mass is of order 0.01–0.1 eV ≈ 10⁻³²–³³ kg. The collective effect of the relic neutrino population within the galactic potential wells of all black holes in the observable universe produces a stochastic gravitational wave background with a characteristic spectrum. This contribution is almost certainly sub-dominant compared to the SMBH binary inspiral background, but it is in principle calculable and could be searched for as a residual in LISA data after the dominant astrophysical backgrounds are modelled and subtracted.

Current pulsar timing arrays, including NANOGrav, have detected a nanohertz SGWB that is not fully accounted for by known sources. While the dominant contribution is almost certainly SMBH binaries, a residual contribution from neutrino orbital decay is calculable and has not, to our knowledge, been specifically modelled or subtracted.

4.2 Weak Interaction Channels

Neutrinos can radiate energy via weak processes during orbital motion. The most relevant is gravitational bremsstrahlung of Z bosons, the neutrino analogue of the electromagnetic bremsstrahlung of charged particles:

ν → ν + Z*  →  ν + f̅f (fermion-antifermion pair)

The cross-section for this process is suppressed by (E/m_Z)⁴ for E ≪ m_Z, making it negligible for cold CνB neutrinos. However, for higher-energy neutrinos produced locally — by supernovae, accretion disc processes, or cosmic-ray interactions near the galactic centre — this channel becomes more relevant.

4.3 Neutrino-Antineutrino Annihilation

The CνB contains approximately equal numbers of neutrinos and antineutrinos. Both populations are captured into shells at similar radii (the gravitational dynamics are identical for particles and antiparticles). The shells therefore contain co-located neutrino and antineutrino populations, enabling:

ν + ν̅ → Z* → e⁺ + e⁻ → 2γ

For cold CνB neutrinos (E_cm ~ 10⁻⁴ eV), the annihilation cross-section off the Z resonance (91 GeV) is suppressed by (E_cm/m_Z)² ≈ 10⁻²⁶ — a suppression so extreme that this channel is entirely negligible for the relic population and makes no measurable contribution to any observed gamma-ray signal. For higher-energy neutrinos produced locally near active galactic nuclei or by supernovae (E ~ MeV to GeV range), the cross-section is less suppressed, but even here the annihilation luminosity from the shells is well below current detection thresholds. This channel is noted for completeness and is not a predicted observable signature with current or near-future instruments.

4.4 The Majorana Discriminant

Whether neutrinos are Dirac particles (neutrino and antineutrino are distinct) or Majorana particles (neutrino is its own antiparticle) is one of the outstanding open questions in particle physics. This distinction has a consequence for the neutrino shell annihilation rate in principle, though the actual relationship is more complex than a simple factor of two: the annihilation enhancement for Majorana neutrinos depends on helicity structure and kinematic regime, and a careful treatment would be required before quantitative predictions could be made. The qualitative point — that the two cases predict different annihilation luminosities from the shells in high-energy neutrino environments near active black holes — is nonetheless noted as a potentially interesting discriminant, complementary to neutrinoless double-beta decay experiments, if the annihilation signal could ever be characterised precisely enough to test it.

5. Observational Signatures and Detectability

We rank the following signatures by estimated detectability, from nearest to current instrument thresholds to furthest. In each case we describe the nature of the signature, the instrument best positioned to detect it, and the estimated timescale.

5.1 Stellar Orbital Residuals Around Sgr A* [Nearest Term]

The S-stars orbiting Sgr A* — in particular S2, tracked with extraordinary precision by the GRAVITY instrument at the VLTI — provide the most exquisite probe of the gravitational potential near a supermassive black hole. The orbit of S2 already shows the relativistic precession predicted by GR, confirmed at high significance.

A distributed neutrino halo around Sgr A* contributes a spherically symmetric additional gravitational potential. Unlike the point-mass contribution of the black hole, a distributed mass shell produces additional precession whose rate depends on the fraction of the total mass enclosed within the stellar orbit. This is analogous to the way the Sun’s equatorial mass distribution produces precession of Mercury beyond the GR contribution.

The predicted additional precession is tiny — for a halo mass fraction of 10⁻¹⁰ of the black hole mass, the effect is at the edge of current measurement precision — but GRAVITY+ and the forthcoming Extremely Large Telescope (ELT) will deliver micro-arcsecond astrometry. Existing S2 data should be re-analysed specifically to constrain or detect this signature. If the halo mass fraction is at the upper end of theoretically expected values, the signal may already be present in existing data.

5.2 Gravitational Wave Background Contribution [LISA/LIGO Band]

The collective gravitational wave emission from neutrino orbital decay within the bound relic populations around black holes produces a stochastic gravitational wave background. The spectral placement is determined by the ISCO orbital frequency of the host black holes. For Sgr A* the ISCO orbital frequency is approximately 0.5–1 mHz, placing GW emission at approximately 1–2 mHz — squarely in the LISA detection band. For stellar-mass black holes (10 M☉), ISCO frequencies are in the kHz range — LIGO/Virgo territory.

It was suggested in an earlier version of this framework that the contribution might appear in pulsar timing array data at nanohertz frequencies. This is incorrect: the frequency mismatch is six to nine orders of magnitude, and the NANOGrav stochastic background is dominated by supermassive black hole binary inspirals at a wholly different mass and frequency scale. That claim is withdrawn.

The correct observational target for the SMBH contribution is LISA, operational in the mid-2030s, which will characterise the millihertz SGWB with sufficient sensitivity to potentially isolate sub-dominant contributions. For stellar-mass black holes, the contribution falls in the LIGO band but is almost certainly unresolvable against the binary merger background. The LISA window is the realistic near-term target.

5.3 Accretion Disc and Jet Spectral Anomalies [Medium Term — Chandra/XRISM/Athena]

Infalling matter and jet material must traverse the neutrino shells on its path to the black hole. While individual neutrino-nucleon scattering events are rare, the shells have been accumulating for billions of years, and the geometry ensures every accreting particle crosses all shell boundaries. The cumulative gravitational back-reaction of the neutrino mass distribution on infalling matter produces subtle but predictable distortions in the accretion disc temperature profile and emissivity at radii corresponding to the shell positions.

The shell radii are calculable from the black hole mass and the neutrino mass eigenvalues. For Sgr A* with mass 4.3 × 10⁶ M☉, the ISCO is at approximately 7.5 × 10⁶ km. The shell radii are slightly larger, with the three mass-eigenstate shells separated by fractional amounts determined by the mass-squared splittings scaled by the neutrino kinetic energy. X-ray observatories (XRISM, currently operating; Athena, 2030s) with high-resolution spectroscopy of the iron K-alpha line and continuum emission could in principle detect radius-specific anomalies if targeted searches are performed at the predicted shell locations.

5.4 Neutrino Flux Lensing and Focal Excesses [Future Neutrino Telescopes]

Black holes gravitationally lens the CνB in the same way they lens light. The lensing geometry for massive particles differs from null geodesic lensing: the deflection angle depends on particle velocity (and hence mass), so different mass eigenstates are deflected differently. This produces mass-eigenstate-dependent focal regions at specific distances from the lensing black hole — a direct manifestation of the spectrometer analogy.

Directional excesses in the diffuse neutrino flux aligned with known black hole positions — detectable by statistical stacking of many sources even if no individual excess is significant — represent a target for next-generation neutrino telescopes including IceCube-Gen2 (in development) and KM3NeT (operational). This signature is the most direct probe of the gravitational neutrino optics described here.

5.5 Gravitational Wave Ringdown Modifications from Merging Halo Systems [LISA, 2030s]

When two black holes merge, their neutrino halos merge dynamically. The final merged black hole carries a combined neutrino halo whose mass distribution is slightly different from a bare black hole of equivalent total mass. The quasinormal mode frequencies of the ringdown — which encode the mass and spin of the final object — are therefore shifted by a small but potentially detectable amount. LISA, designed specifically for supermassive black hole binary mergers, will measure ringdown waveforms with sufficient precision to detect or constrain modifications at the level of fractional mass contributions from the neutrino halo.

6. The Black Hole as Neutrino Mass Spectrometer

A recurring theme in the preceding sections is that the shell stratification encodes information about the neutrino mass eigenstates in the radial coordinate. Current neutrino experiments measure only mass-squared differences. The absolute mass scale is constrained cosmologically (sum < 0.12 eV) but not directly measured. Direct laboratory measurements from tritium beta decay endpoint analyses (KATRIN experiment) are approaching sensitivity to the 0.1 eV scale.

The static shell separation is, however, extremely small. CνB neutrinos at decoupling had identical momenta distributions regardless of mass eigenstate — it is the ratio of momentum to rest mass (i.e., velocity) that differs. In the Newtonian limit, circular orbit radius scales as r_circ ∝ l²/GM where l is specific angular momentum. Since l ∝ v ∝ 1/m for fixed momentum, the fractional shell separation scales as:

Δr/r ≈ -2(Δm/m) × (kT_ν / m_ν)

With kT_ν ≈ 1.7 × 10⁻⁴ eV, m_ν ≈ 0.01–0.1 eV, and Δm/m of order unity in the extreme hierarchy case, the fractional shell separation is of order 10⁻³ to 10⁻⁶ — tiny, and in the fully relativistic regime near the ISCO, further suppressed. Direct spatial resolution of eigenstate shells through gravitational or flux measurements is therefore not a realistic near-term goal.

The spectrometer concept is better understood as a theoretical framework for what the shells encode in principle, rather than a direct measurement programme. A longer-term aspiration — contingent on substantially improved understanding of the wave-packet behaviour of non-relativistic neutrinos in curved spacetime — would be to extract Δm² information from the churning dynamics of the shell structure around a well-characterised black hole. The churning frequency in principle depends on the ratio of oscillation length (encoding Δm²) to orbital parameters (encoding BH mass and geometry), and a measurement of that ratio for a black hole of known mass would, in principle, yield Δm² independently of other methods. This remains a distant theoretical aspiration rather than a near-term observational proposal, particularly given the unsettled treatment of non-relativistic neutrino oscillations noted in Section 3.2.

7. Discussion: Other Implications and Open Questions

7.1 The Galactic Plane Neutrino Flux Anisotropy

The cosmic neutrino background is isotropic to high precision as a cosmological background. However, local neutrino production — from the galactic disc population of stars, supernovae, and compact objects — introduces an anisotropy in the local neutrino flux biased toward the galactic plane. This means that neutrino capture by black holes in the galactic disc is not isotropic: there is a mild excess of infall from the galactic plane direction. The resulting shell structure around disc black holes would be slightly oblate rather than perfectly spherical, with the oblateness correlated with the galactic coordinate of the black hole. This predicted anisotropy in halo morphology is an independent observable, though measuring it is far beyond current capabilities.

7.2 Primordial Black Holes

If primordial black holes (PBHs) contribute a significant fraction of dark matter — a hypothesis that remains observationally viable for certain mass ranges — they would similarly accumulate neutrino halos. PBH neutrino halos would have accumulated since the epoch of matter-radiation equality, potentially much longer than stellar black holes. The gravitational signatures of PBH neutrino halos could contribute to the anomalous mass-to-light ratios observed in some environments, and should be modelled in any comprehensive PBH dark matter search.

7.3 Relationship to Existing CνB Literature

Previous work on CνB-black hole interactions has focused on: (1) gravitational overdensity of relic neutrinos in galactic potential wells as a source of systematic error in cosmological neutrino mass bounds; (2) superradiant extraction of rotational energy from Kerr black holes by bosonic fields, including light neutrino-like particles; and (3) neutrino oscillations in curved spacetime as a test of general relativity. The present framework is distinct from and complementary to all three. We are not aware of prior work treating long-term CνB accumulation into stratified mass-eigenstate shells as a source of conventional astrophysical observables.

8. The Unruh Radiation Angle: Explored and Honestly Assessed

The Unruh effect predicts that an accelerating observer perceives the quantum vacuum not as empty but as a thermal bath of particles at a temperature proportional to the proper acceleration:

T_Unruh = ħa / (2πck_B)

For neutrinos in quasi-circular orbits at the ISCO of a black hole, the relevant acceleration is the local gravitational plus centripetal acceleration. For Sgr A* (M ≈ 4.3 × 10⁶ M☉), the ISCO radius is r_ISCO ≈ 3R_S ≈ 7.5 × 10⁶ km, giving a local acceleration of approximately 3.9 × 10⁵ m/s². The resulting Unruh temperature is:

T_Unruh(Sgr A*) ≈ 1.6 × 10⁻¹⁵ K

For a stellar-mass black hole (10 M☉), tighter curvature raises this to approximately 9.7 × 10⁻¹⁰ K. Both values are negligible against the CνB temperature of 1.95 K and the CMB at 2.7 K. The Unruh thermal bath, in this regime, is effectively invisible against the ambient neutrino background.

Two additional complications reduce the effect further. First, the Unruh effect as conventionally derived requires uniform, eternal linear acceleration. Orbital motion is centripetal — the acceleration vector continuously rotates — introducing ‘circular Unruh’ corrections that typically result in non-thermal or suppressed signatures compared to the linear case. Second, the effect requires sufficient proper time for the thermal bath to fully manifest; if orbital decay or oscillation-driven churning proceeds faster than the coherence timescale, the effect never fully develops. Both factors work against detectability in the current framework.

The honest verdict for 2026 instrumentation: the Unruh angle does not yield a detectable signature in this scenario. It is not a productive observational target with current or immediately foreseeable technology.

However — and this distinction matters — ‘not detectable now’ is not the same as ‘not real’ or ‘not worth pursuing.’ The Unruh effect is a genuine prediction of quantum field theory in curved spacetime. Its reality is not in question; only the magnitude relative to current detector sensitivity. Miguel Alcubierre’s 1994 warp drive metric was considered a piece of entertaining mathematics with no physical relevance; twenty years of theoretical development later, energy condition violations and quantum inequality constraints have been partially addressed and the framework is taken seriously in mainstream theoretical physics. The history of physics is littered with ‘negligibly small’ effects that became central to entirely new fields once instrumentation caught up.

Several specific questions remain genuinely open and theoretically fertile for future investigation:

(1) What is the effective temperature experienced by an orbiting neutrino that accounts simultaneously for the Hawking temperature of the event horizon, the Unruh temperature from orbital acceleration, and the gravitational blueshift of the ambient CνB? These three contributions do not simply add; their interplay in the Kerr metric near the ISCO has not been treated rigorously for this configuration.

(2) Does the interplay between Hawking and Unruh processes create any interference or resonance effects for the shell population that might amplify the otherwise negligible Unruh contribution at specific orbital radii?

(3) For extreme mass ratio inspirals — stellar-mass compact objects spiralling into supermassive black holes, a primary LISA target — the accumulated proper acceleration over the inspiral lifetime is vastly larger than for a quasi-circular orbit. Could the integrated Unruh effect over such an inspiral produce a cumulative correction to the gravitational waveform above LISA’s sensitivity threshold?

(4) Next-generation neutrino detectors operating at sensitivities orders of magnitude beyond IceCube-Gen2, combined with precision black hole characterisation from LISA and ngEHT, may eventually push the accessible temperature floor low enough that effects currently negligible by fifteen orders of magnitude become relevant. This is a long horizon — but it is a horizon, not a wall.

Section 8 therefore closes not with a result but with a bookmark. The Unruh angle is parked, honestly assessed, and left for a generation of instruments we have not yet built.

9. Conclusions

We have presented a framework for the long-term gravitational capture of cosmic background neutrinos by black holes, and the observable consequences of the resulting stratified neutrino halo structure. The core arguments are conservative, resting on confirmed physics: nonzero neutrino mass (established by oscillation experiments), timelike geodesics in general relativity (standard GR), and conservation of energy (non-negotiable). No exotic new physics is invoked.

The principal novel contributions of this paper are:

(1) The neutrino onion: the identification of neutrino mass-eigenstate stratification as a generic feature of the cosmologically bound relic neutrino population around galactic black holes — a result that follows directly from established CνB clustering physics (Ringwald and Wong 2004) extended to BH-scale dynamics.

(2) Oscillation-driven shell churning as a quantum-gravitational phenomenon: the wave-packet breathing picture of a bound neutrino simultaneously delocalised across multiple eigenstate shell radii in the Schwarzschild metric. The specific falsifiable frequency distinction between stellar-mass and supermassive black holes proposed in earlier versions of this framework does not survive the L_osc arithmetic (both regimes are deep in the churning limit by many orders of magnitude) and is withdrawn. The wave-packet concept itself remains valid and worth developing as a standalone thought experiment in curved spacetime quantum mechanics.

(3) A ranked hierarchy of conventional observational signatures. The flagship near-term target is stellar orbital residuals around Sgr A* with GRAVITY+/ELT — geometrically clean, instrument-matched, and independent of the capture mechanism details. The gravitational wave contribution is correctly placed in the LISA millihertz band for SMBHs and the LIGO kHz band for stellar-mass black holes; the previously stated connection to pulsar timing array data was incorrect and is withdrawn.

(4) The Majorana discriminant: the annihilation luminosity of the relic neutrino population near active black holes differs between the Majorana and Dirac cases. The factor-of-two estimate is a simplification; the actual enhancement depends on helicity structure and kinematic regime and requires more careful treatment than presented here.

(5) Honest quantification of the diluteness of the shell population and the explicit correction of the per-BH sweep-up capture framing to the physically correct cosmological clustering picture.

The Unruh radiation angle, which may reveal additional novel signatures at the quantum field theory level, is reserved for subsequent development.

The universe has been building neutrino spectrometers around every black hole for billions of years. The question is whether we are yet good enough at reading them.

Acknowledgements

The authors thank the referees and colleagues who provided critical commentary on earlier drafts of this work.