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A Survey of General Relativistic Magnetohydrodynamic Models for Black Hole Accretion Systems

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper claims SANE accretion flows spin black holes up to a*≈0.94, while magnetically arrested jets can spin them back down.

desk verdict The v3 GRMHD library is a genuinely useful public resource, but the headline spin-equilibrium claim is undermined by an internal inconsistency between the stated a_eq ~ 0.94 and the provided quadratic fit. read the letter →

arxiv 2411.12647 v2 pith:FCXSP4RI submitted 2024-11-19 astro-ph.HE

Vedant Dhruv , Ben Prather , George Wong , Charles F. Gammie This is my paper · ORCID
classification astro-ph.HE
keywords generalrelativisticmagnetohydrodynamicsblackholeaccretionspinequilibriummagneticallyarresteddisksSANEBlandford-ZnajekjetsSagittariusA*numericalsimulations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that a small, carefully chosen library of ten ideal GRMHD simulations can map the two parameters that most control black hole accretion—spin and magnetic flux threading the horizon—onto the fluxes, jet power, and variability that observers can measure. The low-magnetization SANE flows behave like thin disks: their angular momentum and energy fluxes track the standard disk expectation, and they drive the black hole to a spin equilibrium near $a_* \sim 0.94$. The magnetically arrested MAD flows behave differently: prograde cases launch jets that extract angular momentum so efficiently that the black hole spins down, and the fastest-spinning MAD model has an outflow efficiency greater than one, meaning the jet carries away more energy than the accreting gas supplies. The paper also maps the conserved currents of mass, angular momentum, and energy, and shows that MAD disks are sub-Keplerian, hotter, and more variable than SANE disks. These results matter because this is the simulation library used to interpret horizon-scale millimeter observations of the galactic center and other nearby supermassive black holes.

What carries the argument

The load-bearing machinery is the set of conserved currents built from the Killing vectors of the Kerr metric: the mass current $J_M = \sqrt{-g}\,\rho u^\mu$, the angular momentum current $J_L = \sqrt{-g}\,T^\mu{}_\phi$, and the energy current $J_E = -\sqrt{-g}\,T^\mu{}_t$. These are decomposed into electromagnetic and fluid contributions, integrated at the horizon to give specific fluxes $l$ and $e$, and combined into the spin-up parameter $s = l - 2a_*e$, whose sign and zero crossing determine whether a black hole gains or loses spin. The same currents, plotted as time- and azimuth-averaged streamlines, make the Blandford-Znajek extraction pattern visible: inflow in the disk, collimated outflow in the jet.

What would settle it

Rerun the SANE $a_* = +0.94$ simulation at double resolution so the MRI quality factors reach the recommended values, recompute the time-averaged spin-up parameter $s$, and check whether the zero crossing stays at $a_* \approx 0.94$; if it shifts by more than the error bars, the claimed equilibrium is a resolution artifact.

Watch

Extended reading notes

Core claim

The central discovery is that accretion state, not just spin, controls how a black hole evolves. In the SANE models the time-averaged specific angular momentum flux at the horizon matches the thin-disk value at the innermost stable circular orbit, and the spin-up parameter $s = l - 2a_*e$ tracks the thin-disk curve, crossing zero near $a_* \sim 0.94$; the deviations that do appear in prograde models come from fluid thermodynamic forces. In the prograde MAD models the electromagnetic part of the horizon flux dominates, outward Poynting flux is visible along parabolic jet contours anchored at the horizon, and the $a_* = +0.94$ model reaches an outflow efficiency of about $1.5$, so the black hole loses spin. The same data show MAD disks are sub-Keplerian, roughly an order of magnitude hotter than SANE disks inside $r \lesssim 10\,GM/c^2$, and more variable in accretion rate because of intermittent flux eruption events.

Load-bearing premise

The argument assumes that the MRI turbulence that transports angular momentum is resolved well enough that the measured fluxes do not change if the grid is refined; the paper reports MRI quality factors below the recommended values.

Editorial extensions

If this is right

  • If the SANE result holds, any low-magnetization accretion flow will push a black hole toward $a_* \approx 0.94$, regardless of the spin it started with.
  • If the MAD result holds, a prograde, magnetically arrested flow can spin the black hole down, so the observed spin of a source encodes its accretion history, not just its initial spin.
  • An outflow efficiency above one for the highest-spin MAD model means a jet can carry away more mechanical energy than the accreting rest mass supplies, which sets a strict upper limit on the jet power available to accelerate particles.
  • The measured relation between magnetization, spin, and horizon fluxes gives observers a translation table: a horizon image and light curve can be inverted into a preferred accretion state and spin.
  • The strong variability difference between MAD and SANE accretion rates implies that light-curve variability is a cheap observable discriminator between the two states.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • I would treat the $a_* \approx 0.94$ equilibrium as provisional until the SANE runs are repeated at resolution high enough to meet the recommended MRI quality factors, since the paper itself reports being below those levels.
  • A longer-term inference is that black hole spin may settle at an intermediate value if a source alternates between SANE and MAD epochs, because the two states drive spin in opposite directions.
  • The paper's choice of adiabatic index and omission of electron thermodynamics leaves room for the relative temperature of MAD and SANE disks to shift, which would change the synthetic images built from this library.
  • The public data release makes a direct test possible: generate synthetic polarized images from the MAD and SANE snapshots and compare predicted image signatures to upcoming higher-resolution observations.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper presents a library of ten ideal GRMHD simulations of black hole accretion disks, generated with the KHARMA code, spanning five spins (a* = -15/16, -1/2, 0, +1/2, +15/16) and two magnetization states (SANE and MAD). The authors analyze horizon-penetrating mass, angular momentum, and energy fluxes; inflow equilibrium; time-averaged disk structure; conserved currents; jet power; and black hole spin-up/spin-down. The central claims are that SANE disks closely follow thin-disk angular momentum and energy flux expectations and reach spin equilibrium at a* ~ 0.94, while prograde MAD models experience jet-driven spin-down, with the a* = +0.94 MAD having outflow efficiency greater than 1. The simulation data are publicly released, and the paper emphasizes its use in the EHT analysis of Sgr A*.

Significance. If the quantitative claims hold, this library provides a direct numerical mapping from (a*, magnetization) to horizon fluxes and jet powers, which is valuable for interpreting event-horizon-scale observations. The paper is strong in its transparency: it reports MRI quality factors, inflow equilibrium radii, density floor statistics, and measurement choices, and the code and data are publicly available. The qualitative SANE-versus-MAD distinction is robust and consistent with prior work. However, the precision of the headline SANE spin-equilibrium value is currently not supported by the paper's own fit, and the resolution and measurement-radius choices introduce unquantified systematic uncertainties. These issues are local and fixable, but they affect the central mapping claim.

major comments (4)
  1. [§4.6, Eq. (32), Figure 15] The quadratic fit s_fit = -3.267 a*^2 - 8.349 a* + 1.387 has a positive root at a* ~ 0.157, not at a* ~ 0.94. The text states that SANE models achieve spin equilibrium at aeq ~ 0.94, but the provided fit does not substantiate this. If Eq. (32) is intended as a fit to the SANE points, it contradicts the claimed crossing; if it is a fit to the combined sample, it does not provide the SANE-specific crossing. The authors should present a SANE-only fit (or a clear interpolation) with quantified uncertainty, or explicitly state that the equilibrium is inferred by interpolation between a* = +0.5 and a* = +0.94 and justify that inference.
  2. [§4.1.2, first paragraph] The statement 'l > 0 for all spins indicates a net inflow of angular momentum into the black hole' conflicts with the signed definition of l given in the same section. For retrograde spins (a* < 0), the inflowing gas has negative specific angular momentum, so l should be negative. This inconsistency affects the interpretation of Figure 3 and the spin-up analysis in §4.6, and it should be corrected or clarified.
  3. [§3.6, §6] The MRI quality factors in the SANE simulations are Q_theta ~ 5-10 and Q_phi ~ 12-16, below the nominal values of ~10 and ~20, and the paper concedes that the resolution is 'somewhat lower than contemporary studies.' Because the spin-equilibrium result depends on the turbulent stresses that set l and e, the quantitative value aeq ~ 0.94 carries an unquantified resolution uncertainty. The authors should either provide a resolution study of l, e, and s for at least one spin, or explicitly temper the precision of the equilibrium claim.
  4. [§4.2, Table 2 vs §4.5, Table 3] The inflow equilibrium radii are req ~ 18-32 rg for SANE and ~45-66 rg for MAD, yet the jet powers in Table 3 are evaluated at r = 100 rg. For the MAD +0.94 model with outflow efficiency > 1, the region at 100 rg is beyond the inflow equilibrium radius, so the reported Pjet may not be converged. Please quantify the time variability of Pjet at 100 rg or measure it at a radius within the converged region.
minor comments (4)
  1. [Abstract and text] The abstract states '30,000 GM/c^3' where the time unit should be written consistently as GM/c^3 (or tg); the use of GM/c^3 vs GM/c^2 is confusing in a few places.
  2. [§4.1.3] The modulation index M3 is defined, but the error estimate quoted as sigma_M3 / sqrt(27) is not fully explained; please clarify how the number of independent 3-hour segments is derived.
  3. [Table 2] The columns req(Mdot) and req(tin) are not defined in the table note; they are defined in the text but a brief note would aid readability.
  4. [§3.4] The '1DW' primitive recovery scheme is mentioned without a reference; consider adding Noble et al. (2006) or Mignone & McKinney (2007) at that point.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central results are measured simulation fluxes compared against external benchmarks, not predictions derived from fitted inputs.

full rationale

This is a numerical-experiment paper rather than a derivation paper. The central quantities — specific angular momentum flux l, specific energy flux e, and the spin-up parameter s = l - 2a*e — are computed by direct time-averaged integrals of the simulation stress-energy tensor at the horizon (Eqs. 11-14 and 29-30). The SANE spin-equilibrium claim aeq ~ 0.94 is read off the sign of the measured s across the simulated spin points, with thin-disk ISCO values and previous GRMHD results (Gammie et al. 2004; Narayan et al. 2022) used as external comparisons, not as inputs that force the result. The self-citations present (Gammie et al. 2003/2004 for code and prior spin-up study; Wong et al. 2022 for initial-condition implementation; Prather et al. 2021 for the code) support code choices and provide historical context; none of them defines the measured fluxes or jet powers. The jet-power and outflow-efficiency numbers are likewise measured from the simulated stress-energy tensor using a jet definition taken from EHTC M87 V, which is an external observational-analysis benchmark. The skeptic's observation that the quadratic fit in Eq. 32 has a zero near a* ~ 0.16 is a potential internal-consistency or labeling concern about the fit, and the MRI-resolution caveat in Section 6 is a numerical-convergence concern; neither is a case of a prediction reducing by construction to its inputs. The derivation chain is self-contained: outputs are measured, and supporting citations are benchmarks rather than load-bearing circular references.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claims rest on standard GRMHD modeling assumptions and numerical control parameters. No new physical entities are introduced. The most important free parameters are the numerical floors, the adiabatic index, and the quadratic coefficients used to infer the spin equilibrium value.

free parameters (7)
  • Adiabatic index gamma = 4/3
    Chosen to match EHTC SgrA V conventions; the real RIAF plasma is two-temperature with gamma closer to 5/3, which could alter disk thermodynamics.
  • Density floor rho_min = 1e-5
    Numerical floor in code units to prevent negative densities; affects the halo near the BH in MAD models.
  • Internal energy floor u_min = 1e-7
    Numerical floor to keep internal energy positive; used with r^-5/2 scaling.
  • Magnetization ceiling sigma_max = 100
    Ceiling on b^2/rho to avoid primitive recovery failures in the jet funnel.
  • Entropy ceiling kappa_max = 3
    Ceiling on pg/rho^gamma; about 1% of zones hit it.
  • Lorentz factor ceiling Gamma_max = 50
    Limits superluminal velocities in the jet.
  • Spin-up fit coefficients = a=-3.267, b=-8.349, c=1.387
    Quadratic fit to the spin-up parameter s from five SANE simulations; used to infer a_eq~0.94.
assumptions (5)
  • domain assumption Ideal GRMHD equations with infinite conductivity
    Assumes magnetic Reynolds number >>1 and no resistivity; appropriate for RIAFs but misses reconnection and non-thermal particles (Section 2.2).
  • domain assumption Single-temperature fluid with gamma-law equation of state
    Real RIAFs are two-temperature; this affects electron temperature and radiative output, and possibly dynamics (Sections 2.2, 6).
  • ad hoc to paper Fishbone-Moncrief torus initial conditions with a single poloidal magnetic field loop
    Initial conditions chosen for consistency with EHT pipeline; results may depend on this choice (Section 3.2).
  • ad hoc to paper The MRI is resolved well enough to produce converged turbulent stresses
    Q_theta ~5-10 below nominal; the authors acknowledge resolution is lower than contemporary studies (Sections 3.6, 6).
  • ad hoc to paper Inflow equilibrium is reached in the inner region by t=15,000 tg
    They use t=[15,30]e3 tg for averages; req ranges 18-70 rg, so outer regions are not in equilibrium (Section 4.2).

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Cite this review

Pith. "Pith review of A Survey of General Relativistic Magnetohydrodynamic Models for Black Hole Accretion Systems." pith.science (2026). https://pith.science/paper/FCXSP4RI

@misc{pith2026241112647,
  author       = {Pith},
  title        = {Pith review of: A Survey of General Relativistic Magnetohydrodynamic Models for Black Hole Accretion Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FCXSP4RI}},
  note         = {Machine review of arXiv:2411.12647}
}
abstract

General Relativistic Magnetohydrodynamics (GRMHD) simulations are an indispensable tool in studying accretion onto compact objects. The Event Horizon Telescope (EHT) frequently uses libraries of ideal GRMHD simulations to interpret polarimetric, event-horizon-scale observations of supermassive black holes at the centers of galaxies. In this work, we present a library of ten non-radiative, ideal GRMHD simulations that were utilized by the EHT Collaboration in their analysis of Sagittarius A*. The parameter survey explores both low (SANE) and high (MAD) magnetization states across five black hole spins $a_{*}=-15/16,-1/2,0,+1/2,+15/16$ where each simulation was run out to $30,000\hspace{0.1cm}\mathrm{GM/c}^{3}$. We find the angular momentum and energy flux in SANE simulations closely matches the thin-disk value, with minor deviations in prograde models due to fluid forces. This leads to spin equilibrium around $a_{*}\sim0.94$, consistent with previous studies. We study the flow of conserved quantities in our simulations and find mass, angular momentum, and energy transport in SANE accretion flows to be primarily inward and fluid-dominated. MAD models produce powerful jets with outflow efficiency $>1$ for $a_{*}=+0.94$, leading to black hole spin-down in prograde cases. We observe outward directed energy and angular momentum fluxes on the horizon, as expected for the Blandford-Znajek mechanism. MAD accretion flows are sub-Keplerian and exhibit greater variability than their SANE counterpart. They are also hotter than SANE disks within $r\lesssim 10\hspace{0.1cm}\mathrm{GM/c}^{2}$. This study is accompanied by a public release of simulation data at \url{http://thz.astro.illinois.edu/}.

Figures

Figures reproduced from arXiv: 2411.12647 by the authors.

Figure 1
Figure 1. Azimuthal/poloidal slice of initial conditions along with the grid geometry. The color scale denotes the logarithm of the rest-mass density and as an example we plot the magnetic fields structure (in black) for a SANE disk. The grid zone boundaries are represented by the white mesh. The grid zones are concentrated towards the equatorial plane and at smaller radii, where we expect most of the relevant physics to occu… view at source ↗
Figure 2
Figure 2. Time series of the horizon-penetrating fluxes for six models: a∗ = {−15/16, 0, +15/16}, MAD and SANE. Left column: MAD simulations. Right column: SANE simulations. Top row: Rest-mass accretion rate. Second row: Dimensionless magnetic flux. Third row: Normalized, absolute angular momentum flux. Bottom row: Normalized absolute energy flux with the contribution from rest mass subtracted. a∗ = −15/16 simulations are plo… view at source ↗
Figure 3
Figure 3. Time-averaged radial fluxes as a function of black hole spin. The data points in red (blue) denote MAD (SANE) simulations. The dashed line plots the value expected for a thin disk at the ISCO. Left panel: Specific angular momentum flux. Middle panel: Specific energy flux. Right panel: Ratio of outflow power (E˙ − M˙ ) to rest-mass accretion rate [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (17 more)
Figure 4
Figure 4. Figure 4: Similar to [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: 3hr modulation index M3 for the accretion rate M˙ (defined as M∆t ≡ σ∆t/µ∆t; here ∆t = 3hr). To estimate the average M3 (indicated by a marker for each simulation in this plot) for SgrA* (which has a characteristic timescale tg ∼ 20 s), we extract as many independent 3…
Figure 6
Figure 6. Figure 6: Time-averaged, density-weighted radial profiles of tin for the v3 library. The dashed lines are power laws that approximately trace tin. constant α. cs is the local sound speed, and ν is the coefficient of kinematic viscosity. We define req as the radius where the infl…
Figure 7
Figure 7. Figure 7: Top to bottom: time- and azimuth-averaged poloidal plots of ρ, σ ≡ b 2 /ρ, and Θ ≡ pg/(ρc2 ) respectively. Each column represents a different black hole spin. In each subplot, the left panel shows the MAD simulation, while the right panel shows the corresponding SANE s…
Figure 8
Figure 8. Figure 8: Time- and azimuth-averaged “jet profiles” (σ = 1 contours). The solid (dashed) lines represent MAD (SANE) models. The filled grey circle at the lower left corner denotes a zero spin black hole (reh = 2 rg). the Keplerian profile and display a more organized an￾gular mo…
Figure 9
Figure 9. Figure 9: Radial profiles of rest-mass density ρ (in arbitrary code units), dimensionless fluid temperature Θ ≡ pg/(ρc2 ), fluid entropy s, radial velocity v r , specific angular momentum uϕ, specific energy ut, magnetic field strength squared b 2 , inverse plasma-beta β −1 p ≡ …
Figure 10
Figure 10. Figure 10: Angular velocity profiles ⟨Ω⟩ ≡ ⟨u ϕ ⟩/⟨u t ⟩ in Kerr-Schild coordinates in units of deg/GM/c3 . The solid line plots the time-average value and the shaded region plots one standard deviation. The dotted black line is the Kep￾lerian fit ΩK = (r 3/2 + a) −1 for a∗ = +0…
Figure 11
Figure 11. Figure 11: Time- and azimuth-averaged poloidal slices of rest-mass density with averaged conserved currents overlaid for the MAD a∗ = +0.94 model. In the top row we plot (left to right) the mass JM ≡ √ −gρuµ , angular momentum JL ≡ √ −gT µ ϕ , and energy JE ≡ −√ −gT µ t currents…
Figure 12
Figure 12. Figure 12: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]
Figure 14
Figure 14. Figure 14: Similar to [PITH_FULL_IMAGE:figures/full_fig_p018_14.png]
Figure 15
Figure 15. Figure 15: The spin-up parameter ‘s’ given by Equation 30. The markers indicate the time-averaged value and er￾ror bars represent 1σ. Red and blue markers are MAD and SANE simulations respectively. The black dashed line is the expected thin disk values (Equation 31). The solid g…
Figure 16
Figure 16. Figure 16: A time series of the dimensionless magnetic flux crossing the event horizon for all the models in v3. Columns: Left: MAD, Right: SANE simulations. Rows: Top to bottom: Increasing spin from a∗ = −15/16 to a∗ = +15/16. The gray line plots the flux as computed according …
Figure 17
Figure 17. Figure 17: A heat map of the radial component of the mag￾netic field B r at the event horizon for the SANE a∗ = −0.5 simulation. Top panel: B r at a specific instant in time. Bot￾tom panel: B r averaged over the interval t = [25, 30]×103 tg. In both panels, note that B r changes…
Figure 19
Figure 19. Figure 19: A poloidal cut of a MAD simulation illustrating various definitions of a jet or outflow. The background color saturation represents rest-mass density in code units. The goldenrod lines mark geometric boundaries at θ = 1 and θ = π − 1, which are used in this work to co…
Figure 20
Figure 20. Figure 20: Time series of the fraction of total zones where floors and primitive recovery failures occur for MAD a∗ = +0.5. Before accretion begins, geometric floors on ρ and u are the dominant contribution. As the evolution progresses and the funnel region becomes magnetically …
Figure 21
Figure 21. Figure 21: Similar to [PITH_FULL_IMAGE:figures/full_fig_p025_21.png]
Figure 22
Figure 22. Figure 22: A snapshot from the MAD a∗ = +0.5 simu￾lation. Grid zones where σ exceeds σmax are highlighted in red, while the blue contour indicates σ = 1. The underlying grayscale shading shows the logarithm of the rest-mass den￾sity in code units. The exponential radial coordina…

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Forward citations

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Reference graph

Works this paper leans on

170 extracted references · 12 canonical work pages · cited by 3 Pith papers

  1. [1]

    Anile, A. M. 1990, Relativistic Fluids and Magneto-fluids: With Applications in Astrophysics and Plasma Physics, Cambridge Monographs on Mathematical Physics (Cambridge University Press), 10.1017/CBO9780511564130

    doi:10.1017/cbo9780511564130 1990

  2. [2]

    M., & Pennisi, S

    Anile, A. M., & Pennisi, S. 1987, Annales de l'I.H.P. Physique th\'eorique, 46, 27. http://www.numdam.org/item/AIHPA_1987__46_1_27_0/

    1987

  3. [3]

    2012, , 745, L28, 10.1088/2041-8205/745/2/L28

    Asada , K., & Nakamura , M. 2012, , 745, L28, 10.1088/2041-8205/745/2/L28

    doi:10.1088/2041-8205/745/2/l28 2012

  4. [4]

    2022, , 938, 86, 10.3847/1538-4357/ac8a94

    Bacchini , F., Arzamasskiy , L., Zhdankin , V., et al. 2022, , 938, 86, 10.3847/1538-4357/ac8a94

    doi:10.3847/1538-4357/ac8a94 2022

  5. [5]

    A., et al

    Bacchini , F., Zhdankin , V., Gorbunov , E. A., et al. 2024, , 133, 045202, 10.1103/PhysRevLett.133.045202

    doi:10.1103/physrevlett.133.045202 2024

  6. [6]

    A., & Hawley, J

    Balbus, S. A., & Hawley, J. F. 1991, ApJ. . ., 376, 20

    1991

  7. [7]

    Bardeen , J. M. 1970, , 226, 64, 10.1038/226064a0

    doi:10.1038/226064a0 1970

  8. [8]

    M., Press , W

    Bardeen , J. M., Press , W. H., & Teukolsky , S. A. 1972, , 178, 347, 10.1086/151796

    doi:10.1086/151796 1972

Show all 170 references
  1. [9]

    Beckwith , K., & Stone , J. M. 2011, , 193, 6, 10.1088/0067-0049/193/1/6

    2011 doi

  2. [10]

    2017, Astron

    B e \' e thune, W., Lesur, G., & Ferreira, J. 2017, Astron. Astrophys., 600, A75, 10.1051/0004-6361/201630056

    2017 doi

  3. [11]

    S., & Ruzmaikin, A

    Bisnovatyi-Kogan, G. S., & Ruzmaikin, A. A. 1974, , 28, 45, 10.1007/BF00642237

    1974 doi

  4. [12]

    1976, Astrophys Space Sci, 42, 401, 10.1007/BF01225967

    ---. 1976, Astrophys Space Sci, 42, 401, 10.1007/BF01225967

    1976 doi

  5. [13]

    D., & Znajek, R

    Blandford, R. D., & Znajek, R. L. 1977, Monthly Notices of the Royal Astronomical Society, 179, 433, 10.1093/mnras/179.3.433

    1977 doi

  6. [14]

    C., Wright, M

    Bower, G. C., Wright, M. C. H., Falcke, H., & Backer, D. C. 2003, The Astrophysical Journal, 588, 331, 10.1086/373989

    2003 doi

  7. [15]

    R., & Sunderland, D

    Carter Edwards , H., Trott, C. R., & Sunderland, D. 2014, Journal of Parallel and Distributed Computing, 74, 3202, https://doi.org/10.1016/j.jpdc.2014.07.003

    2014 doi

  8. [16]

    N., & Quataert , E

    Chael , A., Lupsasca , A., Wong , G. N., & Quataert , E. 2023, , 958, 65, 10.3847/1538-4357/acf92d

    2023 doi

  9. [17]

    2024, arXiv e-prints, arXiv:2408.04132, 10.48550/arXiv.2408.04132

    Chan , H.-S., & Chan , C.-k. 2024, arXiv e-prints, arXiv:2408.04132, 10.48550/arXiv.2408.04132

    2024 doi arXiv

  10. [18]

    S., Wong , G

    Chan , H.-S., Chan , C.-k., Prather , B. S., Wong , G. N., & Gammie , C. 2024, , 964, 17, 10.3847/1538-4357/ad2454

    2024 doi

  11. [19]

    F., Foucart, F., & Quataert, E

    Chandra, M., Gammie, C. F., Foucart, F., & Quataert, E. 2015, ApJ, 810, 162, 10.1088/0004-637X/810/2/162

    2015 doi

  12. [20]

    2022, The Astrophysical Journal, 941, 30, 10.3847/1538-4357/ac9d97

    Chatterjee, K., & Narayan, R. 2022, The Astrophysical Journal, 941, 30, 10.3847/1538-4357/ac9d97

    2022 doi

  13. [21]

    2020, , 499, 362, 10.1093/mnras/staa2718

    Chatterjee , K., Younsi , Z., Liska , M., et al. 2020, , 499, 362, 10.1093/mnras/staa2718

    2020 doi

  14. [22]

    Choi, E., & Wiita, P. J. 2010, The Astrophysical Journal Supplement Series, 191, 113, 10.1088/0067-0049/191/1/113

    2010 doi

  15. [23]

    S., Baub \"o ck , M., Dhruv , V., et al

    Conroy , N. S., Baub \"o ck , M., Dhruv , V., et al. 2023, , 951, 46, 10.3847/1538-4357/acd2c8

    2023 doi

  16. [24]

    2023, , 959, L3, 10.3847/2041-8213/ad0b79

    Davelaar , J., Ripperda , B., Sironi , L., et al. 2023, , 959, L3, 10.3847/2041-8213/ad0b79

    2023 doi

  17. [25]

    W., & Tchekhovskoy , A

    Davis , S. W., & Tchekhovskoy , A. 2020, , 58, 407, 10.1146/annurev-astro-081817-051905

    2020 doi

  18. [26]

    De Villiers , J.-P., & Hawley , J. F. 2003, , 589, 458, 10.1086/373949

    2003 doi

  19. [27]

    2007, , 473, 11, 10.1051/0004-6361:20077093

    Del Zanna , L., Zanotti , O., Bucciantini , N., & Londrillo , P. 2007, , 473, 11, 10.1051/0004-6361:20077093

    2007 doi

  20. [28]

    M., et al

    Dexter, J., Jiménez-Rosales, A., Ressler, S. M., et al. 2020, Monthly Notices of the Royal Astronomical Society, 494, 4168, 10.1093/mnras/staa922

    2020 doi

  21. [30]

    2009, in astro2010: The Astronomy and Astrophysics Decadal Survey, Vol

    Doeleman , S., Agol , E., Backer , D., et al. 2009, in astro2010: The Astronomy and Astrophysics Decadal Survey, Vol. 2010, 68, 10.48550/arXiv.0906.3899

    2009 doi arXiv

  22. [31]

    M., Lightman , A

    Eardley , D. M., Lightman , A. P., & Shapiro , S. L. 1975, , 199, L153, 10.1086/181871

    1975 doi

  23. [32]

    2023, , 677, A67, 10.1051/0004-6361/202346781

    El Mellah , I., Cerutti , B., & Crinquand , B. 2023, , 677, A67, 10.1051/0004-6361/202346781

    2023 doi

  24. [33]

    2019 a , , 875, L1, ( 87 Paper I), 10.3847/2041-8213/ab0ec7

    Event Horizon Telescope Collaboration , Akiyama , K., Alberdi , A., et al. 2019 a , , 875, L1, ( 87 Paper I), 10.3847/2041-8213/ab0ec7

    2019 doi

  25. [34]

    2019 b , , 875, L2, ( 87 Paper II), 10.3847/2041-8213/ab0c96

    ---. 2019 b , , 875, L2, ( 87 Paper II), 10.3847/2041-8213/ab0c96

    2019 doi

  26. [35]

    2019 c , , 875, L3, ( 87 Paper III), 10.3847/2041-8213/ab0c57

    ---. 2019 c , , 875, L3, ( 87 Paper III), 10.3847/2041-8213/ab0c57

    2019 doi

  27. [36]

    2019 d , , 875, L4, ( 87 Paper IV), 10.3847/2041-8213/ab0e85

    ---. 2019 d , , 875, L4, ( 87 Paper IV), 10.3847/2041-8213/ab0e85

    2019 doi

  28. [37]

    2019 e , , 875, L5, ( 87 Paper V), 10.3847/2041-8213/ab0f43

    ---. 2019 e , , 875, L5, ( 87 Paper V), 10.3847/2041-8213/ab0f43

    2019 doi

  29. [38]

    2019 f , , 875, L6, ( 87 Paper VI), 10.3847/2041-8213/ab1141

    ---. 2019 f , , 875, L6, ( 87 Paper VI), 10.3847/2041-8213/ab1141

    2019 doi

  30. [39]

    C., et al

    Event Horizon Telescope Collaboration , Akiyama , K., Algaba , J. C., et al. 2021 a , , 910, L12, 10.3847/2041-8213/abe71d

    2021 doi

  31. [40]

    2021 b , , 910, L13, 10.3847/2041-8213/abe4de

    ---. 2021 b , , 910, L13, 10.3847/2041-8213/abe4de

    2021 doi

  32. [41]

    2022 a , , 930, L12, 10.3847/2041-8213/ac6674

    Event Horizon Telescope Collaboration , Akiyama , K., Alberdi , A., et al. 2022 a , , 930, L12, 10.3847/2041-8213/ac6674

    2022 doi

  33. [42]

    2022 b , , 930, L13, 10.3847/2041-8213/ac6675

    ---. 2022 b , , 930, L13, 10.3847/2041-8213/ac6675

    2022 doi

  34. [43]

    2022 c , , 930, L14, 10.3847/2041-8213/ac6429

    ---. 2022 c , , 930, L14, 10.3847/2041-8213/ac6429

    2022 doi

  35. [44]

    2022 d , , 930, L15, 10.3847/2041-8213/ac6736

    ---. 2022 d , , 930, L15, 10.3847/2041-8213/ac6736

    2022 doi

  36. [45]

    2022 e , , 930, L16, 10.3847/2041-8213/ac6672

    ---. 2022 e , , 930, L16, 10.3847/2041-8213/ac6672

    2022 doi

  37. [46]

    2022 f , , 930, L17, 10.3847/2041-8213/ac6756

    ---. 2022 f , , 930, L17, 10.3847/2041-8213/ac6756

    2022 doi

  38. [47]

    2023, , 957, L20, 10.3847/2041-8213/acff70

    ---. 2023, , 957, L20, 10.3847/2041-8213/acff70

    2023 doi

  39. [48]

    2024, , 964, L25, 10.3847/2041-8213/ad2df0

    ---. 2024, , 964, L25, 10.3847/2041-8213/ad2df0

    2024 doi

  40. [49]

    G., & Moncrief, V

    Fishbone, L. G., & Moncrief, V. 1976, The Astrophysical Journal, 207, 962, 10.1086/154565

    1976 doi

  41. [50]

    F., Quataert, E., & Tchekhovskoy, A

    Foucart, F., Chandra, M., Gammie, C. F., Quataert, E., & Tchekhovskoy, A. 2017, Monthly Notices of the Royal Astronomical Society, 470, 2240, 10.1093/mnras/stx1368

    2017 doi

  42. [51]

    R., & Raine , D

    Frank , J., King , A. R., & Raine , D. J. 1985, Accretion power in astrophysics

    1985

  43. [52]

    2023, , 130, 115201, 10.1103/PhysRevLett.130.115201

    Galishnikova , A., Philippov , A., Quataert , E., et al. 2023, , 130, 115201, 10.1103/PhysRevLett.130.115201

    2023 doi

  44. [53]

    F., McKinney, J

    Gammie, C. F., McKinney, J. C., & Toth, G. 2003, ApJ, 589, 444, 10.1086/374594

    2003 doi

  45. [54]

    F., & Popham , R

    Gammie , C. F., & Popham , R. 1998, , 498, 313, 10.1086/305521

    1998 doi

  46. [55]

    F., Shapiro , S

    Gammie , C. F., Shapiro , S. L., & McKinney , J. C. 2004, , 602, 312, 10.1086/380996

    2004 doi

  47. [56]

    W., Broderick , A

    Georgiev , B., Pesce , D. W., Broderick , A. E., et al. 2022, , 930, L20, 10.3847/2041-8213/ac65eb

    2022 doi

  48. [57]

    C., Miller , J

    Grete , P., Dolence , J. C., Miller , J. M., et al. 2022, arXiv e-prints, arXiv:2202.12309, 10.48550/arXiv.2202.12309

    2022 doi arXiv

  49. [58]

    F., Guan, X., & Krolik, J

    Hawley, J. F., Guan, X., & Krolik, J. H. 2011, ApJ, 738, 84, 10.1088/0004-637X/738/1/84

    2011 doi

  50. [59]

    F., Richers, S

    Hawley, J. F., Richers, S. A., Guan, X., & Krolik, J. H. 2013, ApJ, 772, 102, 10.1088/0004-637X/772/2/102

    2013 doi

  51. [60]

    F., Grudic , M

    Hopkins , P. F., Grudic , M. Y., Su , K.-Y., et al. 2024, The Open Journal of Astrophysics, 7, 18, 10.21105/astro.2309.13115

    2024

  52. [61]

    Y., & Lefloch , P

    Hou , T. Y., & Lefloch , P. G. 1994, Mathematics of Computation, 62, 497

    1994

  53. [62]

    Howes, G. G. 2010, Monthly Notices of the Royal Astronomical Society: Letters, 409, L104, 10.1111/j.1745-3933.2010.00958.x

    2010

  54. [63]

    1977, ApJ

    Ichimaru, S. 1977, ApJ. . ., 214, 16

    1977

  55. [64]

    V., Narayan, R., & Abramowicz, M

    Igumenshchev, I. V., Narayan, R., & Abramowicz, M. A. 2003, The Astrophysical Journal, 592, 1042, 10.1086/375769

    2003 doi

  56. [65]

    F., Fonseca , R

    Inchingolo , G., Grismayer , T., Loureiro , N. F., Fonseca , R. A., & Silva , L. O. 2018, , 859, 149, 10.3847/1538-4357/aac0f2

    2018 doi

  57. [66]

    2021, Astron

    Jacquemin-Ide, J., Lesur, G., & Ferreira, J. 2021, Astron. Astrophys., 647, A192, 10.1051/0004-6361/202039322

    2021 doi

  58. [67]

    2024, Mon

    Jacquemin-Ide, J., Rincon, F., Tchekhovskoy, A., & Liska, M. 2024, Mon. Not. R. Astron. Soc., 532, 1522, 10.1093/mnras/stae1538

    2024 doi

  59. [68]

    1996, Journal of Computational Physics, 126, 202, https://doi.org/10.1006/jcph.1996.0130

    Jiang, G.-S., & Shu, C.-W. 1996, Journal of Computational Physics, 126, 202, https://doi.org/10.1006/jcph.1996.0130

    1996

  60. [69]

    V., Prather , B

    Joshi , A. V., Prather , B. S., Chan , C.-k., Wielgus , M., & Gammie , C. F. 2024, , 972, 135, 10.3847/1538-4357/ad5b51

    2024 doi

  61. [70]

    V., & Ciolfi, R

    Kastaun, W., Kalinani, J. V., & Ciolfi, R. 2021, Phys. Rev. D, 103, 023018, 10.1103/PhysRevD.103.023018

    2021 doi

  62. [71]

    Kawazura, Y., Barnes, M., & Schekochihin, A. A. 2019, Proc Natl Acad Sci USA, 116, 771, 10.1073/pnas.1812491116

    2019 doi

  63. [72]

    S., et al

    Kim , J.-S., Mueller , H., Nikonov , A. S., et al. 2024, arXiv e-prints, arXiv:2409.00540, 10.48550/arXiv.2409.00540

    2024 doi arXiv

  64. [73]

    Y., Krichbaum , T

    Kim , J. Y., Krichbaum , T. P., Lu , R. S., et al. 2018, , 616, A188, 10.1051/0004-6361/201832921

    2018 doi

  65. [74]

    2003, , 596, L27, 10.1086/379143

    King , A. 2003, , 596, L27, 10.1086/379143

    2003 doi

  66. [75]

    2021, , 92, 101610, 10.1016/j.newar.2021.101610

    Komissarov , S., & Porth , O. 2021, , 92, 101610, 10.1016/j.newar.2021.101610

    2021

  67. [76]

    Komissarov, S. S. 1999, Monthly Notices of the Royal Astronomical Society, 303, 343, 10.1046/j.1365-8711.1999.02244.x

    1999

  68. [77]

    1995, , 33, 581, 10.1146/annurev.aa.33.090195.003053

    Kormendy , J., & Richstone , D. 1995, , 33, 581, 10.1146/annurev.aa.33.090195.003053

    1995

  69. [78]

    W., Schekochihin, A

    Kunz, M. W., Schekochihin, A. A., & Stone, J. M. 2014, Physical Review Letters, 112, 10.1103/physrevlett.112.205003

    2014 doi

  70. [79]

    W., Stone, J

    Kunz, M. W., Stone, J. M., & Quataert, E. 2016, Phys. Rev. Lett., 117, 235101, 10.1103/PhysRevLett.117.235101

    2016 doi

  71. [80]

    1960, Commun

    Lax, P., & Wendroff, B. 1960, Commun. Pure Appl. Math., 13, 217, 10.1002/cpa.3160130205

    1960 doi

  72. [81]

    K., Gammie, C

    Leung, P. K., Gammie, C. F., & Noble, S. C. 2011, Astrophys. J., 737, 21, 10.1088/0004-637X/737/1/21

    2011 doi

  73. [82]

    1967, Relativistic Hydrodynamics and Magnetohydrodynamics

    Lichnerowicz , A. 1967, Relativistic Hydrodynamics and Magnetohydrodynamics

    1967

  74. [83]

    2018, , 474, L81, 10.1093/mnrasl/slx174

    Liska , M., Hesp , C., Tchekhovskoy , A., et al. 2018, , 474, L81, 10.1093/mnrasl/slx174

    2018 doi

  75. [84]

    Liska , M. T. P., Chatterjee , K., Issa , D., et al. 2022, , 263, 26, 10.3847/1538-4365/ac9966

    2022 doi

  76. [85]

    2024, , 960, 82, 10.3847/1538-4357/ad09af

    Lowell , B., Jacquemin-Ide , J., Tchekhovskoy , A., & Duncan , A. 2024, , 960, 82, 10.3847/1538-4357/ad09af

    2024 doi

  77. [86]

    P., et al

    Lu , R.-S., Asada , K., Krichbaum , T. P., et al. 2023, , 616, 686, 10.1038/s41586-023-05843-w

    2023 doi

  78. [87]

    1969, Nature, 223, 690, 10.1038/223690a0

    Lynden-Bell, D. 1969, Nature, 223, 690, 10.1038/223690a0

    1969 doi

  79. [88]

    Lynden-Bell , D., & Pringle , J. E. 1974, , 168, 603, 10.1093/mnras/168.3.603

    1974 doi

  80. [89]

    1998, , 115, 2285, 10.1086/300353

    Magorrian , J., Tremaine , S., Richstone , D., et al. 1998, , 115, 2285, 10.1086/300353

    1998 doi

  81. [90]

    1997, , 490, 605, 10.1086/304908

    Mahadevan , R., & Quataert , E. 1997, , 490, 605, 10.1086/304908

    1997 doi

  82. [91]

    2023, arXiv e-prints, arXiv:2310.11490, 10.48550/arXiv.2310.11490

    Manikantan , V., Kaaz , N., Jacquemin-Ide , J., et al. 2023, arXiv e-prints, arXiv:2310.11490, 10.48550/arXiv.2310.11490

    2023 doi arXiv

  83. [92]

    McKinney , J. C. 2005, , 630, L5, 10.1086/468184

    2005 doi

  84. [93]

    McKinney, J. C. 2006, Monthly Notices of the Royal Astronomical Society, 368, 1561, 10.1111/j.1365-2966.2006.10256.x

    2006

  85. [94]

    C., & Gammie, C

    McKinney, J. C., & Gammie, C. F. 2004, ApJ, 611, 977, 10.1086/422244

    2004 doi

  86. [96]

    Mignone, A., & McKinney, J. C. 2007, Monthly Notices of the Royal Astronomical Society, 378, 1118, 10.1111/j.1365-2966.2007.11849.x

    2007

  87. [97]

    2005, The Astrophysical Journal Supplement Series, 160, 199, 10.1086/430905

    Mignone, A., Plewa, T., & Bodo, G. 2005, The Astrophysical Journal Supplement Series, 160, 199, 10.1086/430905

    2005 doi

  88. [98]

    C., Armitage, P

    Mishra, B., Begelman, M. C., Armitage, P. J., & Simon, J. B. 2020, Mon. Not. R. Astron. Soc., 492, 1855, 10.1093/mnras/stz3572

    2020 doi

  89. [99]

    2013, The Astrophysical Journal Supplement Series, 205, 7, 10.1088/0067-0049/205/1/7

    Mizuno, Y. 2013, The Astrophysical Journal Supplement Series, 205, 7, 10.1088/0067-0049/205/1/7

    2013 doi

  90. [100]

    Mo \'s cibrodzka , M., Falcke , H., Shiokawa , H., & Gammie , C. F. 2014, , 570, A7, 10.1051/0004-6361/201424358

    2014 doi

  91. [101]

    2016, A&A, 586, A38, 10.1051/0004-6361/201526630

    Mościbrodzka, M., Falcke, H., & Shiokawa, H. 2016, A&A, 586, A38, 10.1051/0004-6361/201526630

    2016 doi

  92. [102]

    2022, , 511, 3795, 10.1093/mnras/stac285

    Narayan , R., Chael , A., Chatterjee , K., Ricarte , A., & Curd , B. 2022, , 511, 3795, 10.1093/mnras/stac285

    2022 doi

  93. [103]

    V., & Abramowicz, M

    Narayan, R., Igumenshchev, I. V., & Abramowicz, M. A. 2003, Publications of the Astronomical Society of Japan, 55, L69, 10.1093/pasj/55.6.L69

    2003 doi

  94. [104]

    F., & Kulkarni, A

    Narayan, R., Sądowski, A., Penna, R. F., & Kulkarni, A. K. 2012, Monthly Notices of the Royal Astronomical Society, 426, 3241, 10.1111/j.1365-2966.2012.22002.x

    2012

  95. [105]

    1994, , 428, L13, 10.1086/187381

    Narayan , R., & Yi , I. 1994, , 428, L13, 10.1086/187381

    1994 doi

  96. [106]

    1995, , 444, 231, 10.1086/175599

    ---. 1995, , 444, 231, 10.1086/175599

    1995 doi

  97. [107]

    1995, , 374, 623, 10.1038/374623a0

    Narayan , R., Yi , I., & Mahadevan , R. 1995, , 374, 623, 10.1038/374623a0

    1995 doi

  98. [108]

    M., Porth , O., et al

    Nathanail , A., Fromm , C. M., Porth , O., et al. 2020, , 495, 1549, 10.1093/mnras/staa1165

    2020 doi

  99. [109]

    C., Gammie, C

    Noble, S. C., Gammie, C. F., McKinney, J. C., & Del Zanna, L. 2006, ApJ, 641, 626, 10.1086/500349

    2006 doi

  100. [110]

    C., Krolik, J

    Noble, S. C., Krolik, J. H., & Hawley, J. F. 2010, ApJ, 711, 959, 10.1088/0004-637X/711/2/959

    2010 doi

  101. [111]

    D., & Thorne , K

    Novikov , I. D., & Thorne , K. S. 1973, in Black Holes (Les Astres Occlus), 343--450

    1973

  102. [112]

    N., & Thorne , K

    Page , D. N., & Thorne , K. S. 1974, , 191, 499, 10.1086/152990

    1974 doi

  103. [113]

    Papaloizou , J. C. B., & Lin , D. N. C. 1995, , 33, 505, 10.1146/annurev.aa.33.090195.002445

    1995

  104. [114]

    F., Kulkarni , A., & Narayan , R

    Penna , R. F., Kulkarni , A., & Narayan , R. 2013, , 559, A116, 10.1051/0004-6361/201219666

    2013 doi

  105. [115]

    F., McKinney , J

    Penna , R. F., McKinney , J. C., Narayan , R., et al. 2010, , 408, 752, 10.1111/j.1365-2966.2010.17170.x

    2010

  106. [116]

    Popham , R., & Gammie , C. F. 1998, , 504, 419, 10.1086/306054

    1998 doi

  107. [117]

    2017, Computational Astrophysics and Cosmology, 4, 1, 10.1186/s40668-017-0020-2

    Porth , O., Olivares , H., Mizuno , Y., et al. 2017, Computational Astrophysics and Cosmology, 4, 1, 10.1186/s40668-017-0020-2

    2017 doi

  108. [118]

    2019, The Astrophysical Journal Supplement Series, 243, 26, 10.3847/1538-4365/ab29fd

    Porth, O., Chatterjee, K., Narayan, R., et al. 2019, The Astrophysical Journal Supplement Series, 243, 26, 10.3847/1538-4365/ab29fd

    2019 doi

  109. [119]

    2022, Ph.D

    Prather, B. 2022, Ph.D. Thesis

    2022

  110. [120]

    Prather, B. S. 2024, arXiv, 10.48550/arXiv.2408.01361

    2024 doi arXiv

  111. [121]

    S., Wong, G

    Prather, B. S., Wong, G. N., Dhruv, V., et al. 2021, Journal of Open Source Software, 6, 3336, 10.21105/joss.03336

    2021 doi

  112. [122]

    Pringle , J. E. 1981, , 19, 137, 10.1146/annurev.aa.19.090181.001033

    1981

  113. [123]

    2000, , 545, 842, 10.1086/317845

    Quataert , E., & Gruzinov , A. 2000, , 545, 842, 10.1086/317845

    2000 doi

  114. [124]

    J., Begelman , M

    Rees , M. J., Begelman , M. C., Blandford , R. D., & Phinney , E. S. 1982, , 295, 17, 10.1038/295017a0

    1982 doi

  115. [125]

    M., Tchekhovskoy, A., Quataert, E., Chandra, M., & Gammie, C

    Ressler, S. M., Tchekhovskoy, A., Quataert, E., Chandra, M., & Gammie, C. F. 2015, Mon. Not. R. Astron. Soc., 454, 1848, 10.1093/mnras/stv2084

    2015 doi

  116. [126]

    M., Tchekhovskoy , A., Quataert , E., & Gammie , C

    Ressler , S. M., Tchekhovskoy , A., Quataert , E., & Gammie , C. F. 2017, , 467, 3604, 10.1093/mnras/stx364

    2017 doi

  117. [127]

    M., White , C

    Ressler , S. M., White , C. J., & Quataert , E. 2023, , 521, 4277, 10.1093/mnras/stad837

    2023 doi

  118. [128]

    M., White , C

    Ressler , S. M., White , C. J., Quataert , E., & Stone , J. M. 2020, , 896, L6, 10.3847/2041-8213/ab9532

    2020 doi

  119. [129]

    A., Bender , R., et al

    Richstone , D., Ajhar , E. A., Bender , R., et al. 1998, , 385, A14, 10.48550/arXiv.astro-ph/9810378

    1998 doi arXiv

  120. [130]

    Ripperda , B., Bacchini , F., & Philippov , A. A. 2020, , 900, 100, 10.3847/1538-4357/ababab

    2020 doi

  121. [131]

    2022, , 924, L32, 10.3847/2041-8213/ac46a1

    Ripperda , B., Liska , M., Chatterjee , K., et al. 2022, , 924, L32, 10.3847/2041-8213/ac46a1

    2022 doi

  122. [132]

    2018, The Astrophysical Journal, 854, 132, 10.3847/1538-4357/aaa6d1

    Riquelme, M., Quataert, E., & Verscharen, D. 2018, The Astrophysical Journal, 854, 132, 10.3847/1538-4357/aaa6d1

    2018 doi

  123. [133]

    A., Quataert, E., & Verscharen, D

    Riquelme, M. A., Quataert, E., & Verscharen, D. 2016, The Astrophysical Journal, 824, 123, 10.3847/0004-637x/824/2/123

    2016 doi

  124. [134]

    E., Sironi, L., & Narayan, R

    Rowan, M. E., Sironi, L., & Narayan, R. 2017, ApJ, 850, 29, 10.3847/1538-4357/aa9380

    2017 doi

  125. [135]

    1962, USSR Computational Mathematics and Mathematical Physics, 1, 304, https://doi.org/10.1016/0041-5553(62)90062-9

    Rusanov, V. 1962, USSR Computational Mathematics and Mathematical Physics, 1, 304, https://doi.org/10.1016/0041-5553(62)90062-9

    1962 doi

  126. [136]

    R., Ressler, S

    Ryan, B. R., Ressler, S. M., Dolence, J. C., Gammie, C., & Quataert, E. 2018, The Astrophysical Journal, 864, 126, 10.3847/1538-4357/aad73a

    2018 doi

  127. [137]

    R., Ressler, S

    Ryan, B. R., Ressler, S. M., Dolence, J. C., et al. 2017, The Astrophysical Journal, 844, L24, 10.3847/2041-8213/aa8034

    2017 doi

  128. [138]

    Salas , L. D. S., Musoke , G., Chatterjee , K., et al. 2024, , 533, 254, 10.1093/mnras/stae1834

    2024 doi

  129. [139]

    J., & Stone, J

    Sano, T., Inutsuka, S., Turner, N. J., & Stone, J. M. 2004, ApJ, 605, 321, 10.1086/382184

    2004 doi

  130. [140]

    C., & Dexter, J

    Scepi, N., Begelman, M. C., & Dexter, J. 2023, Monthly Notices of the Royal Astronomical Society, 527, 1424, 10.1093/mnras/stad3299

    2023 doi

  131. [141]

    Scepi , N., Dexter , J., & Begelman , M. C. 2022, , 511, 3536, 10.1093/mnras/stac337

    2022 doi

  132. [142]

    I., & Sunyaev , R

    Shakura , N. I., & Sunyaev , R. A. 1973, , 24, 337

    1973

  133. [143]

    Shapiro , S. L. 2005, , 620, 59, 10.1086/427065

    2005 doi

  134. [144]

    L., Lightman , A

    Shapiro , S. L., Lightman , A. P., & Eardley , D. M. 1976, , 204, 187, 10.1086/154162

    1976 doi

  135. [145]

    C., Gammie, C

    Shiokawa, H., Dolence, J. C., Gammie, C. F., & Noble, S. C. 2012, ApJ, 744, 187, 10.1088/0004-637X/744/2/187

    2012 doi

  136. [146]

    Silk , J., & Rees , M. J. 1998, , 331, L1, 10.48550/arXiv.astro-ph/9801013

    1998 doi arXiv

  137. [147]

    2015, , 800, 89, 10.1088/0004-637X/800/2/89

    Sironi , L. 2015, , 800, 89, 10.1088/0004-637X/800/2/89

    2015 doi

  138. [148]

    2015, The Astrophysical Journal, 800, 88, 10.1088/0004-637x/800/2/88

    Sironi, L., & Narayan, R. 2015, The Astrophysical Journal, 800, 88, 10.1088/0004-637x/800/2/88

    2015 doi

  139. [149]

    2013, , 429, 3533, 10.1093/mnras/sts632

    S a dowski , A., Narayan , R., Tchekhovskoy , A., & Zhu , Y. 2013, , 429, 3533, 10.1093/mnras/sts632

    2013 doi

  140. [150]

    2017, , 466, 705, 10.1093/mnras/stw3116

    S a dowski , A., Wielgus , M., Narayan , R., et al. 2017, , 466, 705, 10.1093/mnras/stw3116

    2017 doi

  141. [151]

    M., & Gardiner , T

    Stone , J. M., & Gardiner , T. 2009, , 14, 139, 10.1016/j.newast.2008.06.003

    2009 doi

  142. [152]

    2013, Monthly Notices of the Royal Astronomical Society, 436, 3856, 10.1093/mnras/stt1881

    Sądowski, A., Narayan, R., Penna, R., & Zhu, Y. 2013, Monthly Notices of the Royal Astronomical Society, 436, 3856, 10.1093/mnras/stt1881

    2013 doi

  143. [153]

    Tchekhovskoy, A., & McKinney, J. C. 2012, Monthly Notices of the Royal Astronomical Society: Letters, 423, L55, 10.1111/j.1745-3933.2012.01256.x

    2012

  144. [154]

    C., & Narayan, R

    Tchekhovskoy, A., McKinney, J. C., & Narayan, R. 2012, J. Phys.: Conf. Ser., 372, 012040, 10.1088/1742-6596/372/1/012040

    2012 doi

  145. [155]

    Tchekhovskoy , A., Narayan , R., & McKinney , J. C. 2010, , 711, 50, 10.1088/0004-637X/711/1/50

    2010 doi

  146. [156]

    Tchekhovskoy, A., Narayan, R., & McKinney, J. C. 2011, Monthly Notices of the Royal Astronomical Society: Letters, 418, L79, 10.1111/j.1745-3933.2011.01147.x

    2011

  147. [157]

    2024, Astrophys

    The Event Horizon Telescope Collaboration , Akiyama, K., Alberdi, A., et al. 2024, Astrophys. J. Lett., 964, L26, 10.3847/2041-8213/ad2df1

    2024 doi

  148. [158]

    Thorne , K. S. 1974, , 191, 507, 10.1086/152991

    1974 doi

  149. [159]

    2000, Journal of Computational Physics, 161, 605

    T \'o th, G. 2000, Journal of Computational Physics, 161, 605

    2000

  150. [160]

    2021, Computing in Science & Engineering, 23, 10, 10.1109/MCSE.2021.3098509

    Trott, C., Berger-Vergiat, L., Poliakoff, D., et al. 2021, Computing in Science & Engineering, 23, 10, 10.1109/MCSE.2021.3098509

    2021

  151. [161]

    R., Lebrun-Grandié, D., Arndt, D., et al

    Trott, C. R., Lebrun-Grandié, D., Arndt, D., et al. 2022, IEEE Transactions on Parallel and Distributed Systems, 33, 805, 10.1109/TPDS.2021.3097283

    2022

  152. [162]

    T., Olivares , H., Cerutti , B., & Mo \'s cibrodzka , M

    Vos , J. T., Olivares , H., Cerutti , B., & Mo \'s cibrodzka , M. 2024, , 531, 1554, 10.1093/mnras/stae1046

    2024 doi

  153. [163]

    C., Hardee , P

    Walker , R. C., Hardee , P. E., Davies , F. B., Ly , C., & Junor , W. 2018, , 855, 128, 10.3847/1538-4357/aaafcc

    2018 doi

  154. [164]

    R., Uzdensky, D

    Werner, G. R., Uzdensky, D. A., Begelman, M. C., Cerutti, B., & Nalewajko, K. 2018, Monthly Notices of the Royal Astronomical Society, 473, 4840, 10.1093/mnras/stx2530

    2018 doi

  155. [165]

    J., Quataert , E., & Gammie , C

    White , C. J., Quataert , E., & Gammie , C. F. 2020, , 891, 63, 10.3847/1538-4357/ab718e

    2020 doi

  156. [166]

    J., Stone , J

    White , C. J., Stone , J. M., & Quataert , E. 2019, , 874, 168, 10.3847/1538-4357/ab0c0c

    2019 doi

  157. [167]

    2022, Astrophys

    Wielgus, M., Marchili, N., Mart \' -Vidal, I., et al. 2022, Astrophys. J. Lett., 930, L19, 10.3847/2041-8213/ac6428

    2022 doi

  158. [168]

    Wilson, L. A. 2017, Big Data Research, 8, 57, https://doi.org/10.1016/j.bdr.2017.04.001

    2017 doi

  159. [169]

    N., Du, Y., Prather, B

    Wong, G. N., Du, Y., Prather, B. S., & Gammie, C. F. 2021, The Astrophysical Journal, 914, 55, 10.3847/1538-4357/abf8b8

    2021 doi

  160. [170]

    N., Prather, B

    Wong, G. N., Prather, B. S., Dhruv, V., et al. 2022, The Astrophysical Journal Supplement Series, 259, 64, 10.3847/1538-4365/ac582e

    2022 doi

  161. [171]

    2015, , 804, 101, 10.1088/0004-637X/804/2/101

    Yuan , F., Gan , Z., Narayan , R., et al. 2015, , 804, 101, 10.1088/0004-637X/804/2/101

    2015 doi

  162. [172]

    A., & Kunz, M

    Zhdankin, V., Uzdensky, D. A., & Kunz, M. W. 2021, ApJ, 908, 71, 10.3847/1538-4357/abcf31

    2021 doi

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