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REVIEW 3 major objections 3 minor 66 references

Magnetic fields around merging black holes can boost proton collisions to 10^17–10^20 eV, placing binary mergers among the candidate sources of the most energetic cosmic rays.

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2026-08-01 07:35 UTC pith:4LSQH5XW

load-bearing objection Useful parameter scan of the magnetized BSW mechanism, but the UHECR-source claim fails on the escape-energy budget: E_cm at the horizon is not energy at infinity. the 3 major comments →

arxiv 2607.21385 v1 pith:4LSQH5XW submitted 2026-07-23 astro-ph.HE astro-ph.COgr-qchep-phhep-th

Ultra-High-Energy Particle Production in Binary Mergers Endowed with Magnetic Fields

Carlos H. Coimbra-Araujo , Rita C. Anjos , Jonas P. Pereira , Jaziel G. Coelho This is my paper
classification astro-ph.HE astro-ph.COgr-qchep-phhep-th PACS 04.70.-s98.70.Sa
keywords ultra-high-energy cosmic raysBanados-Silk-West mechanismmagnetized Kerr spacetimebinary black hole mergersneutron star mergerscenter-of-mass energygravitational-wave eventsmagnetic field amplification
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that the magnetized remnants of compact binary mergers—black hole–neutron star binaries, charged black hole binaries, and post-merger black holes from neutron star coalescences—act as natural accelerators of ultra-high-energy cosmic rays. By solving the equations of motion for charged particles in a magnetized Kerr spacetime with fields of 10^12–10^14 G, the authors show that proton–proton collisions near the horizon reach center-of-mass energies of roughly 10^18–10^20 eV. The magnetic field widens the parameter space of the Banados–Silk–West mechanism, which in vacuum requires nearly extremal spin; here spins as low as 0.7 suffice. Applied to 34 high-spin gravitational-wave events, the model predicts event-specific maximum energies, with the most massive and rapidly spinning remnants reaching about 10^20 eV. If correct, this turns gravitational-wave observatories and cosmic-ray detectors into joint probes of near-horizon magnetic fields.

Core claim

The central claim is that a magnetic field anchored in the merger environment transforms the Banados–Silk–West (BSW) effect from a fine-tuned theoretical curiosity into a generic acceleration channel. Solving the modified geodesic equations for charged particles in Kerr spacetime with a uniform magnetic field, the authors find that collisions within 10^-10 M of the horizon produce center-of-mass energies up to ~10^20 eV for remnant masses 20–150 M_sun and spins χ_f ~0.7–0.9. The field acts as an amplifier: the energy scales as E_max = m_0 c^2 (M/M_sun) F(χ_f, B, ℓ_1, ℓ_2), with the amplification function F growing roughly as B^0.3–0.5 in the magnetic-dominated regime B > 10^13 G, reaching fa

What carries the argument

The central object is the Banados–Silk–West (BSW) effect—the near-horizon collision of two particles whose near-critical angular momenta produce unbounded center-of-mass energies in an extremal Kerr spacetime—extended to a magnetized Kerr black hole. The carrying mechanism is the modified geodesic equation with a Lorentz force, using the uniform-field four-potential A_ϕ = B g_ϕϕ/2, which shifts the effective potential and creates new families of critical orbits that remove the fine-tuning on spin. The paper introduces a dimensionless amplification function F(χ_f, B, ℓ_1, ℓ_2) that encodes how much the magnetic field raises the maximum E_cm as a function of spin, field strength, and the angul

Load-bearing premise

The results rest on treating the near-horizon magnetic field as locally uniform with four-potential A_ϕ = B g_ϕϕ/2 all the way down to 10^-10 M from the horizon at field strengths up to 10^14 G, a description whose validity the paper asserts but does not demonstrate at field strengths where the magnetic force overwhelms gravity.

What would settle it

Compute whether a uniform field with A_ϕ = B g_ϕϕ/2 is consistent with a force-free magnetosphere around a spinning black hole at radii r = r_H + 10^-10 M: if the actual field geometry deviates from uniform on the scale of the proton Larmor radius (which is orders of magnitude smaller than M), the resonant angular-momentum tuning that produces the 10^20 eV energies is destroyed. Alternatively, trace the collision products' trajectories to infinity in the same spacetime; if the outgoing particles are gravitationally redshifted below 10^18 eV before escaping, the claimed UHECR energies never rea

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the mechanism operates as claimed, magnetized BH–NS binaries and post-merger black holes from neutron star coalescences join AGN jets and gamma-ray bursts as viable UHECR sources, with an energy scale set directly by the remnant mass and spin.
  • The BSW effect no longer requires near-extremal spin: with B ≳ 10^12 G, ultra-high-energy collisions occur for χ_f ≳ 0.7, so the mechanism should operate across most of the observed merger population rather than in rare fine-tuned configurations.
  • The predicted correlation between gravitational-wave remnant parameters and UHECR energies—such as the ~1.6×10^20 eV maximum for the most massive, highest-spin event—provides event-by-event targets for joint gravitational-wave and cosmic-ray searches.
  • The three identified acceleration regimes imply that even neutron-star-scale fields (10^12–10^13 G) double to quintuple the collision energy, making magnetic enhancement a generic feature of mergers involving neutron stars rather than an exotic occurrence.
  • The approximate linear scaling E_max ∝ M favors the most massive stellar-origin remnants (M ≳ 100 M_sun) as the sources of the highest-energy cosmic rays near 10^20 eV, a trend already visible across the 34-event catalog.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If pre-merger UHECR production is prompt and directional, the highest-energy cosmic rays might be traceable to individual past mergers within their magnetic-deflection horizon, making the UHECR sky a fossil record of binary coalescences—an extension the paper does not explicitly develop.
  • Because the collision energy scales with the rest mass of the projectile, heavier nuclei would yield even higher E_max than the conservative proton case; the scenario thereby naturally predicts a heavy or mixed composition at the highest energies, which can be checked against cosmic-ray observatory composition measurements.
  • The same machinery, applied to intermediate-mass black holes merging with neutron stars, would push maximum energies beyond 10^20 eV; this is an unexplored prediction that follows directly from the paper's scaling relations but is not stated in it.
  • A direct test of the central assumption is to compare the uniform-field results with general-relativistic magnetohydrodynamic simulations of post-merger magnetospheres: if the near-horizon field is not approximately uniform on the collision scale, the predicted amplification and therefore the UHECR energies would be reduced.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper studies proton–proton collisions in the immediate vicinity of magnetized Kerr black holes as a possible UHECR production site via the BSW effect. It solves the equations of motion for charged test particles in a Kerr spacetime with a uniform magnetic field (four-potential A_phi = B g_phi_phi/2), fixes the conserved energy per particle to E_i/m0=1, scans black hole mass, spin, magnetic field, and angular momenta, and computes the local center-of-mass energy E_cm. It reports E_cm up to ~10^20 eV for M~100 M_sun, χ~0.9, B~10^14 G, identifies three magnetic-field regimes, and applies the results to 34 LIGO-Virgo-KAGRA remnants with χ_f>0.7, giving event-by-event predictions.

Significance. The paper is systematic and transparent: it writes down the equations of motion (Eqs. 12–16), states its assumptions (equatorial orbits, uniform field, E_i/m0=1), and provides a parameter scan tied to a specific GW catalog. If the claimed connection were valid, it would link binary-merger observations to UHECR production and offer testable correlations between remnant spin/mass and maximum particle energy. The authors also correctly identify that the standard BSW mechanism is fine-tuned and that magnetic fields can broaden the parameter space. However, the central astrophysical conclusion does not follow from the calculation, because the computed E_cm is a local invariant, not the energy of particles escaping to infinity.

major comments (3)
  1. [Secs. II.B, II.F, IV; Abstract] The paper's central claim that magnetized binaries are 'promising sources of UHECRs' is not supported by the computed quantity. With the stationary four-potential A_phi = B g_phi_phi/2 and A_t=0 (Sec. II.B) and E_i/m0=1 (Sec. II.F), the conserved canonical energy of each proton is m_p c^2; the total energy of the two-particle system at infinity is 2 m_p c^2. The high E_cm is a local invariant near the horizon, not an energy available to escaping debris. Any outgoing product has energy at infinity bounded by the total conserved energy plus a possible small Penrose-type negative-energy contribution, i.e., at most a few GeV, not 10^20 eV. The paper explicitly defers escape modeling (Sec. IV), but the deferred step is not a technical detail: within the stated model, the UHECR-source claim cannot follow. The citation of Refs. [27–30] does not address this because the A_phi-only field has no e
  2. [Eq. (18)] The claimed linear mass scaling E_max = m0 c^2 (M/M_sun) F(χ_f, B, ℓ1, ℓ2) conflicts with the standard BSW scaling, in which E_cm/m0 is independent of M for fixed dimensionless angular momenta and spin. In a magnetized Kerr spacetime the only dimensionless magnetic parameter is q B M / m0, so any M-dependence in E_cm/m0 must come through that combination, not through an explicit factor M/M_sun attributed to 'the geometric nature of the gravitational acceleration mechanism' (Sec. II.E). Since Table I uses this scaling to assign event-by-event energies, the catalog predictions require re-derivation. The text should either justify Eq. (18) from the equations of motion or replace it with the correct dimensionless scaling.
  3. [Sec. II.B, Fig. 1] The uniform-field potential is specified as A_phi = B g_phi_phi/2 with a single non-vanishing component; this is not the standard uniform-field solution in Kerr, which also has A_t = B g_t_phi/2. Moreover, at B~10^14 G the Larmor radius of a 10^20 eV proton is ~10 m, far smaller than the gravitational radius ~10^5 m, so the Lorentz force dominates the trajectory and the BSW effect (a gravitational geodesic resonance) is not the relevant mechanism. The paper does not demonstrate that the local uniform-field approximation is valid from the ISCO down to ε=10^-10 M, nor that the collision products can leave the strong-field region. This affects the interpretation of the 'magnetic-dominated' regime and the claimed order-of-magnitude enhancement.
minor comments (3)
  1. [Table I caption] The caption states 34 events with χ_f>0.7, but the table includes GW170817 with χ_f≤0.89 (upper limit, not a measurement) and log10 E = '–'. Clarify whether this BNS event is counted in the 34 and why it satisfies the selection criterion.
  2. [Eq. (19)] Equation (19) writes E_max in terms of M/100M_sun and χ_f/0.9, but the amplification function F is not given in closed form; it would aid reproducibility to state whether F is evaluated at the fiducial B=10^14 G and which (ℓ1, ℓ2) values are used.
  3. [Sec. III] The numerical optimization over (ℓ1, ℓ2) is described only as 'systematically vary[ing] the angular momenta'; the grid spacing and convergence criteria are not given, which matters because Figs. 1 and 3 exhibit 'bumpiness' attributed to grid-sampling artifacts.

Circularity Check

0 steps flagged

No significant circularity: the energy predictions are computed parameter-scan outputs, not fitted inputs; self-citations are not load-bearing and the main limitation (escape modeling) is a physical correctness issue rather than a circular derivation.

full rationale

The derivation chain is self-contained. The paper defines a magnetized Kerr test-particle setup via Eq. (9), adopts the explicit four-potential A_phi = B g_phi_phi/2, solves for the four-velocity components (12)-(14), and evaluates the center-of-mass invariant (16) as a function of (M, chi_f, B, epsilon, l1, l2). The claimed E_cm ~ 1e18-1e20 eV and the Table I entries are outputs of this explicit calculation, after a systematic scan/optimization over angular momenta, not quantities fitted to UHECR data. Eq. (18) is a scaling rewrite of the same E_cm expression rather than a separate fitted law; it contains no new empirical input. The strong-field regime B ~ 1e12-1e14 G is an input assumption, motivated by the authors' prior Letter [37] and by GRMHD/merger literature, but the present paper does not rely on [37] to supply the collision-energy result itself, and [37] is an independent published calculation rather than a self-referential uniqueness or ansatz theorem. The most serious weakness is the openly acknowledged omission in Sec. IV: 'We have focused on collision energies near the horizon without detailed modeling of particle escape...' This prevents the local E_cm from being translated into escaping UHECR energies, especially given E_i/m0 = 1 and A_t = 0, but this is a physical/correctness gap in the UHECR-source inference, not a case where a prediction reduces to its inputs by definition. No circular step of any enumerated kind is present.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claim rests on the assumed existence of very strong, ordered magnetic fields near merger remnant horizons and on the validity of a uniform-field approximation for particle trajectories at those strengths; both are asserted rather than derived from independent evidence.

free parameters (4)
  • Magnetic field strength B = 10^14 G (fiducial)
    Adopted as an upper-limit field, motivated by speculative scenarios; the results are shown for a range 10^10–10^14 G.
  • Radial offset ε = 10^-10 M
    Choice of collision radius near horizon; energies drop for larger ε (Fig. 1a).
  • Particle angular momenta ℓ1, ℓ2 = optimized (e.g., 1.5, -1.5 in fiducial runs)
    The maximum energy is found by scanning these within Eq. (17); the reported Emax is the maximum over these.
  • Particle energy ratios E_i/m0 = 1
    Fixed by hand; the paper does not explore infall energies other than the marginally bound value.
axioms (5)
  • standard math Kerr metric describes the remnant spacetime (Boyer-Lindquist coordinates)
    Invoked throughout Sec. II.A.
  • standard math Charged particles obey the Lorentz-force equation (Eq. 9)
    Used to derive four-velocity components in Sec. II.B.
  • domain assumption Magnetic fields of order 10^12–10^14 G exist in the near-horizon region of merger remnants
    Stated as 'plausible' and 'motivated by extreme scenarios'; supported by references to MHD simulations for BNS, but for BBHs requires a charged BH with q/m ~ 10^-4–10^-3, which the authors note is an open question.
  • ad hoc to paper Uniform magnetic field with A_ϕ = B g_ϕϕ/2 is a valid local approximation for the entire region of interest
    Adopted in Sec. II.B; the authors themselves call it a local approximation but then apply it globally from ISCO to near horizon.
  • domain assumption Collision debris can escape to be observed as UHECRs
    Not modeled; the paper computes only E_cm near the horizon and defers escape modeling (Sec. IV).

pith-pipeline@v1.3.0-alltime-deepseek · 234 in / 15795 out tokens · 200121 ms · 2026-08-01T07:35:47.705845+00:00 · methodology

0 comments
read the original abstract

We study the production of ultra-high-energy particles via the Ba\~nados--Silk--West (BSW) mechanism in the pre-merger phase of binary systems detected by LIGO-Virgo-KAGRA. By solving the geodesic equations for charged particles in magnetized Kerr spacetime with fields of $B \sim 10^{12}$--$10^{14}$~G, we demonstrate that collisions near the horizon can achieve center-of-mass energies $E_{\mathrm{cm}} \sim 10^{18}$-- $10^{20}$~eV, placing them firmly in the ultra-high-energy cosmic-ray (UHECR) range. We systematically explore the parameter space of merger remnants, varying black hole mass ($M \sim 20$--$150\,M_\odot$, characteristic of the binary black hole population), dimensionless spin ($\chi_f \sim 0.7$--$0.9$), magnetic field strength, and particle angular momenta. Our analysis reveals three distinct acceleration regimes: a gravity-dominated regime ($B < 10^{12}$~G) with negligible magnetic enhancement; a transition regime ($10^{12}~\text{G} \lesssim B \lesssim 10^{13}~\text{G}$) where gravitational and magnetic effects compete; and a magnetic-dominated regime ($B > 10^{13}$~G) where fields amplify collision energies by nearly an order of magnitude. For the 34 gravitational-wave events with high remnant spins ($\chi_f > 0.7$), we compute the maximum achievable energies, finding that systems with $\chi_f \gtrsim 0.85$ and $M \gtrsim 100\,M_\odot$ can reach $E_{\mathrm{max}} \sim 10^{20}$~eV. Our results establish magnetized binary mergers, particularly black hole--neutron star systems and postmerger black hole remnants formed in binary neutron star coalescences, as promising sources of UHECRs and provide quantitative predictions linking gravitational-wave observables to particle acceleration efficiency.

Figures

Figures reproduced from arXiv: 2607.21385 by Carlos H. Coimbra-Araujo, Jaziel G. Coelho, Jonas P. Pereira, Rita C. Anjos.

Figure 1
Figure 1. Figure 1: (a) shows Ecm as a function of the magnetic field for a fixed mass M = 10 M⊙ and spin χf = 0.9, varying the radial offset in the interval ε = (10−6 – 10−12)M. For weak fields, B <∼ 1011 G, the dependence on ε is modest, with Ecm ranging between ∼ 1012 and 1016 eV as the collision point is moved closer to the hori￾zon. For stronger fields, B >∼ 1012 G, the effect of the radial offset becomes more pronounced… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

66 extracted references · 44 linked inside Pith

  1. [1]

    Fenˆ omenos Extremos do Universo

    andℓ 2 (particle 2). The collisions occur near the horizon atr=r H +εwithε= 10 −10Mfor a magnetised Kerr black hole of massM= 50M ⊙, spin parameterχ f = 0.9, and magnetic fieldB= 10 12 G. White dashed lines indicateℓ 1 = 0 and ℓ2 = 0, while the red dashed diagonal marksℓ 1 =ℓ 2, along which the configuration is symmetric under the exchange of the two part...

    2025

  2. [2]

    Aabet al.(Pierre Auger), Measurement of the cosmic- ray energy spectrum above 2.5×10 18 eV using the Pierre Auger Observatory, Phys

    A. Aabet al.(Pierre Auger), Measurement of the cosmic- ray energy spectrum above 2.5×10 18 eV using the Pierre Auger Observatory, Phys. Rev. D102, 062005 (2020), arXiv:2008.06486 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  3. [3]

    Abu-Zayyadet al., The Cosmic-Ray Energy Spectrum Observed with the Surface Detector of the Telescope Ar- ray Experiment, ApJL768, L1 (2013), arXiv:1205.5067 [astro-ph.HE]

    T. Abu-Zayyadet al., The Cosmic-Ray Energy Spectrum Observed with the Surface Detector of the Telescope Ar- ray Experiment, ApJL768, L1 (2013), arXiv:1205.5067 [astro-ph.HE]

    Pith/arXiv arXiv 2013

  4. [4]

    Kotera and A

    K. Kotera and A. V. Olinto, The Astrophysics of Ultrahigh-Energy Cosmic Rays, ARAA49, 119 (2011), arXiv:1101.4256 [astro-ph.HE]

    Pith/arXiv arXiv 2011

  5. [5]

    L. A. Anchordoqui, Ultra-high-energy cosmic rays, Physics Reports801, 1 (2019), arXiv:1807.09645 [astro- ph.HE]

    Pith/arXiv arXiv 2019

  6. [6]

    Greisen, End to the Cosmic-Ray Spectrum?, PRL16, 748 (1966)

    K. Greisen, End to the Cosmic-Ray Spectrum?, PRL16, 748 (1966). 15

    1966

  7. [7]

    G. T. Zatsepin and V. A. Kuz’min, Upper Limit of the Spectrum of Cosmic Rays, Soviet Journal of Experimen- tal and Theoretical Physics Letters4, 78 (1966)

    1966

  8. [8]

    Mayotte, Measurement and Interpretation of UHECR Mass Composition at the Pierre Auger Ob- servatory, arXiv e-prints , arXiv:2507.10292 (2025), arXiv:2507.10292 [astro-ph.HE]

    E. Mayotte, Measurement and Interpretation of UHECR Mass Composition at the Pierre Auger Ob- servatory, arXiv e-prints , arXiv:2507.10292 (2025), arXiv:2507.10292 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  9. [9]

    A. Halimet al.(Pierre Auger Collaboration), Inference of the Mass Composition of Cosmic Rays with Ener- gies from 1018.5 to 1020 eV Using the Pierre Auger Ob- servatory and Deep Learning, PRL134, 021001 (2025), arXiv:2406.06315 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  10. [10]

    Fraschetti, On the acceleration of ultra-high- energy cosmic rays, Philosophical Transactions of the Royal Society of London Series A366, 4417 (2008), arXiv:0809.3057 [astro-ph]

    F. Fraschetti, On the acceleration of ultra-high- energy cosmic rays, Philosophical Transactions of the Royal Society of London Series A366, 4417 (2008), arXiv:0809.3057 [astro-ph]

    Pith/arXiv arXiv 2008

  11. [11]

    A. R. Bell, The acceleration of cosmic rays in shock fronts - I., MNRAS182, 147 (1978)

    1978

  12. [12]

    A. R. Bell, Cosmic ray acceleration, Astroparticle Physics 43, 56 (2013), arXiv:1301.7041 [astro-ph.HE]

    Pith/arXiv arXiv 2013

  13. [13]

    Spitkovsky, Particle acceleration in relativistic colli- sionless shocks: Fermi process at last?, Astrophys

    A. Spitkovsky, Particle acceleration in relativistic colli- sionless shocks: Fermi process at last?, Astrophys. J. Lett.682, L5 (2008), arXiv:0802.3216 [astro-ph]

    Pith/arXiv arXiv 2008

  14. [14]

    Caprioli and A

    D. Caprioli and A. Spitkovsky, Simulations of ion ac- celeration at non-relativistic shocks. i. acceleration ef- ficiency, Astrophys. J.783, 91 (2014), arXiv:1310.2943 [astro-ph.HE]

    Pith/arXiv arXiv 2014

  15. [15]

    N. W. Schween, F. Schulze, and B. Reville, Sapphire++: A particle transport code combining a spherical har- monic expansion and the discontinuous Galerkin method, Journal of Computational Physics523, 113690 (2025), arXiv:2501.05110 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  16. [16]

    Shirin T, B

    A. Shirin T, B. Reville, N. W. Schween, F. Schulze, and J. G. Kirk, Spectral curvature and breaks from Fermi ac- celeration at oblique shocks, MNRAS544, L160 (2025), arXiv:2511.01635 [astro-ph.HE]

    arXiv 2025

  17. [17]

    R. J. Protheroe and T. Stanev, Cut-offs and pile-ups in shock acceleration spectra, Astroparticle Physics10, 185 (1999), arXiv:astro-ph/9808129 [astro-ph]

    Pith/arXiv arXiv 1999

  18. [18]

    L. N. Padilha and R. C. Dos Anjos, Oblique Shocks at Supernova Remnants in Massive Star Clusters: A Model for the Cosmic-Ray Knee Observed by LHAASO, ApJ 1002, 97 (2026), arXiv:2604.07977 [astro-ph.HE]

    Pith/arXiv arXiv 2026

  19. [19]

    C. H. Coimbra Araujo and R. C. Anjos, Rotating black holes with magnetic fields as accelerators of charged par- ticles, inInternational Conference on Black Holes as Cosmic Batteries: UHECRs and Multimessenger Astron- omy. 12-15 September 2018. Foz do Igua¸ cu(2018) p. 5

    2018

  20. [20]

    C. H. Coimbra-Ara´ ujo and R. C. Anjos, Acceleration of charged particles from near-extremal rotating black holes embedded in magnetic fields, Classical and Quan- tum Gravity38, 015007 (2021), arXiv:2005.13599 [gr-qc]

    Pith/arXiv arXiv 2021

  21. [21]

    C. H. Coimbra-Ara´ ujo and R. C. dos Anjos, Ultra-High- Energy Particles at the Border of Kerr Black Holes Trig- gered by Magnetocentrifugal Winds, Galaxies10, 84 (2022)

    2022

  22. [22]

    Ba˜ nados, J

    M. Ba˜ nados, J. Silk, and S. M. West, Kerr Black Holes as Particle Accelerators to Arbitrarily High Energy, PRL 103, 111102 (2009), arXiv:0909.0169 [hep-ph]

    Pith/arXiv arXiv 2009

  23. [23]

    J. M. Bardeen, W. H. Press, and S. A. Teukolsky, Ro- tating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation, ApJ178, 347 (1972)

    1972

  24. [24]

    Jacobson and T

    T. Jacobson and T. P. Sotiriou, Spinning Black Holes as Particle Accelerators, PRL104, 021101 (2010), arXiv:0911.3363 [gr-qc]

    Pith/arXiv arXiv 2010

  25. [25]

    Wei, Y.-X

    S.-W. Wei, Y.-X. Liu, H. Guo, and C.-E. Fu, Charged spinning black holes as particle accelerators, PRD82, 103005 (2010), arXiv:1006.1056 [hep-th]

    Pith/arXiv arXiv 2010

  26. [26]

    V. P. Frolov, Weakly magnetized black holes as parti- cle accelerators, PRD85, 024020 (2012), arXiv:1110.6274 [gr-qc]

    Pith/arXiv arXiv 2012

  27. [27]

    Igata, T

    T. Igata, T. Harada, and M. Kimura, Effect of a weak electromagnetic field on particle acceleration by a rotat- ing black hole, PRD85, 104028 (2012), arXiv:1202.4859 [gr-qc]

    Pith/arXiv arXiv 2012

  28. [28]

    Bejger, T

    M. Bejger, T. Piran, M. Abramowicz, and F. H ˚ akanson, Collisional Penrose Process near the Horizon of Ex- treme Kerr Black Holes, PRL109, 121101 (2012), arXiv:1205.4350 [astro-ph.HE]

    Pith/arXiv arXiv 2012

  29. [29]

    O. B. Zaslavskii, Energetics of particle collisions near dirty rotating extremal black holes: Banados-Silk-West effect versus Penrose process, PRD86, 084030 (2012), arXiv:1205.4410 [gr-qc]

    Pith/arXiv arXiv 2012

  30. [30]

    Harada, H

    T. Harada, H. Nemoto, and U. Miyamoto, Upper limits of particle emission from high-energy collision and reaction near a maximally rotating kerr black hole, Phys. Rev. D 86, 024027 (2012)

    2012

  31. [31]

    J. D. Schnittman, Revised Upper Limit to Energy Ex- traction from a Kerr Black Hole, PRL113, 261102 (2014), arXiv:1410.6446 [astro-ph.HE]

    Pith/arXiv arXiv 2014

  32. [32]

    O. B. Zaslavskii, Unbounded energies of debris from head-on particle collisions near black holes, Modern Physics Letters A30, 1550076 (2015), arXiv:1411.0267 [gr-qc]

    Pith/arXiv arXiv 2015

  33. [33]

    Berti, R

    E. Berti, R. Brito, and V. Cardoso, Ultrahigh-Energy Debris from the Collisional Penrose Process, PRL114, 251103 (2015), arXiv:1410.8534 [gr-qc]

    Pith/arXiv arXiv 2015

  34. [34]

    O. B. Zaslavskii, Ultrahigh energy particle collisions near the black hole horizon in the strong magnetic field, Modern Physics Letters A29, 1450112 (2014), arXiv:1403.6286 [gr-qc]

    Pith/arXiv arXiv 2014

  35. [35]

    Ehlert, F

    D. Ehlert, F. Oikonomou, and E. Peretti, Ultra- high-energy cosmic rays from ultra-fast outflows of active galactic nuclei, MNRAS539, 2435 (2025), arXiv:2411.05667 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  36. [36]

    G. R. Farrar, Binary Neutron Star Mergers as the Source of the Highest Energy Cosmic Rays, PRL134, 081003 (2025), arXiv:2405.12004 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  37. [37]

    G. R. Farrar, Ultra-High-energy Cosmic Ray Production in Binary Neutron Star Mergers, ApJL994, L7 (2025), arXiv:2506.22625 [astro-ph.HE]

    arXiv 2025

  38. [38]

    J. P. Pereira, C. H. Coimbra-Ara´ ujo, R. C. dos An- jos, and J. G. Coelho, Binary Coalescences as Sources of Ultrahigh-Energy Cosmic Rays, PRL132, 091401 (2024), arXiv:2307.06200 [astro-ph.HE]

    Pith/arXiv arXiv 2024

  39. [39]

    R. Abbottet al.(LIGO Scientific Collaboration and Virgo Collaboration), GWTC-2: Compact Binary Co- alescences Observed by LIGO and Virgo during the First Half of the Third Observing Run, Phys. Rev. X11, 021053 (2021), arXiv:2010.14527 [gr-qc]

    Pith/arXiv arXiv 2021

  40. [40]

    R. Abbottet al.(LIGO Scientific Collaboration and Virgo Collaboration), GWTC-3: Compact Binary Co- alescences Observed by LIGO and Virgo during the Sec- ond Part of the Third Observing Run, Phys. Rev. X13, 041039 (2023), arXiv:2111.03606 [gr-qc]. 16

    Pith/arXiv arXiv 2023

  41. [41]

    R. Abbottet al.(LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration), Population of Merging Compact Binaries Inferred Using Gravita- tional Waves through GWTC-3, Phys. Rev. X13, 011048 (2023), arXiv:2111.03634 [astro-ph.HE]

    Pith/arXiv arXiv 2023

  42. [42]

    Zilh˜ ao, V

    M. Zilh˜ ao, V. Cardoso, C. Herdeiro, L. Lehner, and U. Sperhake, Collisions of charged black holes, PRD85, 124062 (2012), arXiv:1205.1063 [gr-qc]

    Pith/arXiv arXiv 2012

  43. [43]

    Obergaulinger, M

    M. Obergaulinger, M. A. Aloy, and E. M¨ uller, Local simulations of the magnetized Kelvin-Helmholtz insta- bility in neutron-star mergers, A&A515, A30 (2010), arXiv:1003.6031 [astro-ph.SR]

    Pith/arXiv arXiv 2010

  44. [44]

    Giacomazzo, J

    B. Giacomazzo, J. Zrake, P. C. Duffell, A. I. MacFadyen, and R. Perna, Producing Magnetar Magnetic Fields in the Merger of Binary Neutron Stars, ApJ809, 39 (2015), arXiv:1410.0013 [astro-ph.HE]

    Pith/arXiv arXiv 2015

  45. [45]

    Kiuchi, Y

    K. Kiuchi, Y. Sekiguchi, K. Kyutoku, M. Shibata, K. Taniguchi, and T. Wada, High resolution magnetohy- drodynamic simulation of black hole-neutron star merger: Mass ejection and short gamma ray bursts, PRD92, 064034 (2015), arXiv:1506.06811 [astro-ph.HE]

    Pith/arXiv arXiv 2015

  46. [46]

    M. Ruiz, R. N. Lang, V. Paschalidis, and S. L. Shapiro, Binary Neutron Star Mergers: A Jet Engine for Short Gamma-Ray Bursts, ApJL824, L6 (2016), arXiv:1604.02455 [astro-ph.HE]

    Pith/arXiv arXiv 2016

  47. [47]

    Palenzuela, R

    C. Palenzuela, R. Aguilera-Miret, F. Carrasco, R. Ciolfi, J. V. Kalinani, W. Kastaun, B. Mi˜ nano, and D. Vigan` o, Turbulent magnetic field amplification in binary neutron star mergers, Phys. Rev. D106, 023013 (2022)

    2022

  48. [48]

    Radice, S

    D. Radice, S. Bernuzzi, and A. Perego, The Dynamics of Binary Neutron Star Mergers and GW170817, Annual Review of Nuclear and Particle Science70, 95 (2020), arXiv:2002.03863 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  49. [49]

    Aguilera-Miret, J.-E

    R. Aguilera-Miret, J.-E. Christian, S. Rosswog, and C. Palenzuela, Robustness of Magnetic Field Amplifica- tion in Neutron Star Mergers, MNRAS542, 3067 (2025), arXiv:2504.10604 [astro-ph.HE]

    arXiv 2025

  50. [50]

    Ciolfi, The key role of magnetic fields in binary neu- tron star mergers, General Relativity and Gravitation52, 59 (2020), arXiv:2003.07572 [astro-ph.HE]

    R. Ciolfi, The key role of magnetic fields in binary neu- tron star mergers, General Relativity and Gravitation52, 59 (2020), arXiv:2003.07572 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  51. [51]

    Margalit and B

    B. Margalit and B. D. Metzger, Constraining the Maxi- mum Mass of Neutron Stars from Multi-messenger Ob- servations of GW170817, ApJL850, L19 (2017)

    2017

  52. [52]

    Shibata and K

    M. Shibata and K. Hotokezaka, Merger and Mass Ejec- tion of Neutron-Star Binaries, Annual Review of Nuclear and Particle Science69, 41 (2019)

    2019

  53. [53]

    V. P. Frolov, Weakly magnetized black holes as particle accelerators, PRD85, 024020 (2012)

    2012

  54. [54]

    O. B. Zaslavskii, Acceleration of particles by black holes: General considerations, PRD82, 083004 (2010)

    2010

  55. [55]

    Kiuchi, K

    K. Kiuchi, K. Kyutoku, Y. Sekiguchi, and M. Shibata, Global simulations of strongly magnetized remnant mas- sive neutron stars formed in binary neutron star mergers, Phys. Rev. D97, 124039 (2018)

    2018

  56. [56]

    Foucart, A

    F. Foucart, A. Chernoglazov, M. Boyle, T. Hinderer, M. Miller, J. Moxon, M. A. Scheel, N. Deppe, M. D. Duez, F. H´ ebert, L. E. Kidder, W. Throwe, and H. P. Pfeiffer, High-accuracy waveforms for black hole-neutron star systems with spinning black holes, PRD103, 064007 (2021), arXiv:2010.14518 [gr-qc]

    Pith/arXiv arXiv 2021

  57. [57]

    Falcke and L

    H. Falcke and L. Rezzolla, Fast radio bursts: the last crack of doom, A&A562, A137 (2014)

    2014

  58. [58]

    B. P. Abbottet al., Multi-messenger Observations of a Binary Neutron Star Merger, ApJL848, L12 (2017)

    2017

  59. [59]

    E. W. Leaver, An analytic representation for the quasi- normal modes of kerr black holes, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences402, 285 (1985)

    1985

  60. [60]

    Berti, V

    E. Berti, V. Cardoso, and A. O. Starinets, Quasinormal modes of black holes and black branes, Classical and Quantum Gravity26, 163001 (2009), arXiv:0905.2975 [gr-qc]

    Pith/arXiv arXiv 2009

  61. [61]

    Reitze, R

    D. Reitze, R. X. Adhikari, S. Ballmer, B. Barish, L. Bar- sotti, G. Billingsley, D. A. Brown, Y. Chen, D. Coyne, R. Eisenstein, M. Evans, P. Fritschel, E. D. Hall, A. Laz- zarini, G. Lovelace, J. Read, B. S. Sathyaprakash, D. Shoemaker, J. Smith, C. Torrie, S. Vitale, R. Weiss, C. Wipf, and M. Zucker, Cosmic Explorer: The U.S. Contribution to Gravitationa...

    Pith/arXiv arXiv 2019

  62. [62]

    Maggiore, C

    M. Maggiore, C. Van Den Broeck, N. Bartolo, E. Bel- gacem, D. Bertacca, M. A. Bizouard, M. Branch- esi, S. Clesse, S. Foffa, J. Garc ´ ıa-Bellido, S. Grimm, J. Harms, T. Hinderer, S. Matarrese, C. Palomba, M. Peloso, A. Ricciardone, and M. Sakellariadou, Science case for the Einstein telescope, JCAP2020, 050 (2020), arXiv:1912.02622 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  63. [63]

    G. A. Anastasi and Pierre Auger Collaboration, Auger- Prime: The Pierre Auger Observatory upgrade, Nuclear Instruments and Methods in Physics Research A1044, 167497 (2022)

    2022

  64. [64]

    A. V. Olinto, J. Krizmanic, J. H. Adams, R. Aloisio, L. A. Anchordoqui, A. Anzalone, M. Bagheri, D. Bargh- ini, M. Battisti, D. R. Bergman,et al., The poemma (probe of extreme multi-messenger astrophysics) obser- vatory, J. Cosmology Astropart. Phys.2021, 007 (2021), arXiv:2012.07945 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  65. [65]

    Alvarez-Mu˜ niz, R

    GRAND Collaboration, J. Alvarez-Mu˜ niz, R. Alves Batista, A. Balagopal V., J. Bonˇ cius, M. Bustamante, W. Carvalho, D. Charrier, I. Cog- nard, V. Decoene,et al., The giant radio array for neutrino detection (grand): Science and design, Science China Physics, Mechanics, and Astronomy63, 219501 (2020), arXiv:1810.09994 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  66. [66]

    S. C. de L´ eonet al.(CREDO Collaboration), Cosmic-ray extremely distributed observatory, Symmetry12, 1835 (2020)

    2020