Recognition: 2 theorem links
· Lean TheoremFirst M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
Pith reviewed 2026-05-12 11:20 UTC · model grok-4.3
The pith
The Event Horizon Telescope has imaged the shadow of the supermassive black hole in M87, matching general relativity predictions for a Kerr black hole.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Using a global array of radio telescopes operating at 1.3 mm wavelength, the central compact source in M87 is resolved into an asymmetric bright emission ring of diameter 42 ± 3 μas with a central brightness depression of flux ratio ~10:1. This image remains stable across four observing days and different processing methods. It matches ray-traced simulations of general-relativistic magnetohydrodynamic flows around a Kerr black hole, yielding a mass estimate of (6.5 ± 0.7) × 10^9 solar masses. The brightness asymmetry is attributed to relativistic beaming from plasma orbiting near the speed of light.
What carries the argument
The black hole shadow, formed by the gravitational bending of light rays and the capture of photons within the event horizon, which creates a dark central region surrounded by a bright photon ring in the observed image.
If this is right
- The derived black hole mass provides an independent measurement consistent with stellar dynamics estimates.
- Relativistic effects in the plasma explain the observed ring asymmetry without additional assumptions.
- This imaging technique can be extended to probe black hole properties in other galaxies.
- It establishes very long baseline interferometry at millimeter wavelengths as a tool for direct tests of general relativity.
Where Pith is reading between the lines
- Similar shadows might be detectable in other active galactic nuclei with sufficient resolution.
- Time-lapse observations could reveal the dynamics of the accretion flow and test for deviations from Kerr geometry.
- Polarization measurements in future data could constrain the magnetic field structure near the black hole.
Load-bearing premise
The dark central region results from photon capture at the event horizon instead of being obscured by dense, non-emitting plasma features not included in the simulation models.
What would settle it
Detection of significant emission filling the central depression at 1.3 mm wavelength, or a ring diameter that deviates substantially from the size expected for a black hole of the estimated mass under general relativity.
read the original abstract
When surrounded by a transparent emission region, black holes are expected to reveal a dark shadow caused by gravitational light bending and photon capture at the event horizon. To image and study this phenomenon, we have assembled the Event Horizon Telescope, a global very long baseline interferometry array observing at a wavelength of 1.3 mm. This allows us to reconstruct event-horizon-scale images of the supermassive black hole candidate in the center of the giant elliptical galaxy M87. We have resolved the central compact radio source as an asymmetric bright emission ring with a diameter of 42+/-3 micro-as, which is circular and encompasses a central depression in brightness with a flux ratio ~10:1. The emission ring is recovered using different calibration and imaging schemes, with its diameter and width remaining stable over four different observations carried out in different days. Overall, the observed image is consistent with expectations for the shadow of a Kerr black hole as predicted by general relativity. The asymmetry in brightness in the ring can be explained in terms of relativistic beaming of the emission from a plasma rotating close to the speed of light around a black hole. We compare our images to an extensive library of ray-traced general-relativistic magnetohydrodynamic simulations of black holes and derive a central mass of M = (6.5+/-0.7) x 10^9 Msun. Our radio-wave observations thus provide powerful evidence for the presence of supermassive black holes in centers of galaxies and as the central engines of active galactic nuclei. They also present a new tool to explore gravity in its most extreme limit and on a mass scale that was so far not accessible.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports the first Event Horizon Telescope (EHT) observations at 1.3 mm of the supermassive black hole candidate in M87. It reconstructs an asymmetric bright emission ring of diameter 42 ± 3 μas that is circular and encloses a central brightness depression with a flux ratio of ~10:1. The ring diameter and width are recovered consistently across four observations on different days and multiple independent calibration and imaging pipelines. Comparison to an extensive library of ray-traced GRMHD simulations supports consistency with the expected shadow of a Kerr black hole, with the ring asymmetry attributed to relativistic beaming from near-light-speed plasma rotation, and yields a central mass of M = (6.5 ± 0.7) × 10^9 M⊙.
Significance. If the interpretation holds, this is a landmark result providing the first resolved image of event-horizon-scale structure around a supermassive black hole and direct evidence supporting the Kerr-shadow prediction of general relativity. The multi-pipeline and multi-epoch consistency strengthens the robustness of the image reconstruction itself. The simulation comparison enables a mass estimate that is independent of stellar dynamics, reinforcing the identification of supermassive black holes as AGN central engines and opening a new regime for strong-field gravity tests.
major comments (1)
- [§5 and §6] §5 and §6: The central claim that the observed ~10:1 central depression and 42 ± 3 μas ring are consistent with the Kerr shadow (arising from photon capture inside the unstable photon orbit) depends on the GRMHD simulation library spanning all plausible 1.3 mm emission geometries. The manuscript should explicitly quantify the coverage of the library with respect to optical depth, electron distribution functions, and inner-disk structures, and discuss whether unmodeled optically thick plasma could produce an equivalent ring-plus-depression morphology without invoking photon capture.
minor comments (2)
- [Abstract] The abstract states the ring is 'circular' while the main text notes asymmetry in brightness; a brief clarification on the distinction between geometric circularity and brightness asymmetry would improve precision.
- Figure captions and text should explicitly state the exact number of independent imaging pipelines and the quantitative stability metrics (e.g., rms variation in diameter) across the four epochs to allow readers to assess robustness without cross-referencing supplementary material.
Simulated Author's Rebuttal
We thank the referee for their positive evaluation of the manuscript and for the constructive major comment. We address the point on the GRMHD simulation library coverage below and agree that additional explicit quantification and discussion will strengthen the presentation of our results.
read point-by-point responses
-
Referee: [§5 and §6] §5 and §6: The central claim that the observed ~10:1 central depression and 42 ± 3 μas ring are consistent with the Kerr shadow (arising from photon capture inside the unstable photon orbit) depends on the GRMHD simulation library spanning all plausible 1.3 mm emission geometries. The manuscript should explicitly quantify the coverage of the library with respect to optical depth, electron distribution functions, and inner-disk structures, and discuss whether unmodeled optically thick plasma could produce an equivalent ring-plus-depression morphology without invoking photon capture.
Authors: The simulation library spans a broad range of 1.3 mm emission geometries, including variations in optical depth (from optically thin to moderately optically thick regimes), electron distribution functions (thermal Maxwell-Jüttner distributions as well as hybrid thermal/non-thermal models), and inner-disk structures (different magnetic field topologies, accretion rates, and disk inclinations). These parameters are described in the companion simulation papers referenced in §5. We will revise the manuscript to add an explicit quantitative summary (e.g., a table or paragraph listing the explored ranges of optical depth at 1.3 mm and electron temperature) in §6. On the question of unmodeled optically thick plasma, our library already includes models with significant optical depth; in those cases the central depression persists due to gravitational lensing and photon capture at the photon orbit, while the ring diameter and asymmetry remain consistent with the observed image. Emission geometries lacking strong lensing and photon capture (e.g., purely optically thick disks without relativistic beaming) do not reproduce the measured ring diameter of 42 μas or the ~10:1 brightness contrast. We will add a concise discussion paragraph in §6 making these points explicit while noting that the library covers the main physically plausible parameter space for M87 at 1.3 mm. revision: partial
Circularity Check
No significant circularity; derivation chain is self-contained
full rationale
The image reconstruction proceeds directly from raw VLBI visibility data via multiple independent calibration and imaging pipelines, producing a stable 42±3 μas ring and ~10:1 central depression without reference to the final mass or GR shadow interpretation. The mass M=(6.5±0.7)×10^9 M⊙ is obtained by scaling the observed angular diameter against an external library of ray-traced GRMHD simulations whose size-to-mass relation is fixed by general relativity and the independently measured distance to M87; this is a standard parameter estimation step, not a prediction that feeds back into the data reduction or assumes the conclusion by construction. No load-bearing self-citations, self-definitional steps, or ansätze imported from prior author work appear in the provided derivation chain. The consistency claim follows from morphological match to the predicted photon-orbit shadow rather than definitional equivalence.
Axiom & Free-Parameter Ledger
free parameters (1)
- Black hole mass M =
(6.5 +/- 0.7) x 10^9 Msun
axioms (2)
- domain assumption General relativity holds in the strong-field regime and predicts a photon ring and shadow for a Kerr black hole.
- domain assumption The radio emission originates from a transparent plasma region whose brightness distribution is well approximated by the GRMHD simulation library.
Lean theorems connected to this paper
-
IndisputableMonolith.Foundation.AlexanderDualityalexander_duality_circle_linking echoes?
echoesECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.
We have resolved the central compact radio source as an asymmetric bright emission ring with a diameter of 42±3 μas, which is circular and encompasses a central depression in brightness with a flux ratio ≳10:1. ... the observed image is consistent with expectations for the shadow of a Kerr black hole as predicted by general relativity.
-
IndisputableMonolith.Foundation.RealityFromDistinctionreality_from_one_distinction unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
We compare our images to an extensive library of ray-traced general-relativistic magnetohydrodynamic simulations of black holes and derive a central mass of M = (6.5±0.7)×10^9 M⊙.
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Forward citations
Cited by 38 Pith papers
-
Spin-Induced Nonlinear Scalarization of Kerr Black Holes in Einstein-scalar-Gauss-Bonnet Gravity
Kerr black holes in an EsGB model without linear instability undergo nonlinear scalarization above spin 0.5, existing in a finite low-mass high-spin wedge rather than a narrow band.
-
GRMHD accretion beyond the black hole paradigm: Light from within the shadow
3D GRMHD simulations of accretion onto a JMN-1 horizonless singularity produce a magnetically arrested disk with an accretion rate of ~3e-6 Eddington matching M87* observations and EHT-consistent images, plus central ...
-
Analog regular black holes and black hole mimickers for surface-gravity waves in fluids
Surface-gravity waves in shallow water can be configured with central and graded drainage to analogize regular black holes and mimickers, enabling lab study of their instabilities.
-
Kinetic magnetohydrodynamics and Landau fluid closure in relativity
The authors derive relativistic drift-kinetic moment equations and a new analytic Landau fluid closure that incorporates anisotropic heat conduction and Landau damping without assuming collisional thermalization.
-
Demagnetizing KBR and New Ricci-flat Rotating Metric
Demagnetizing the KBR solution produces a new Ricci-flat rotating metric with deformation parameter B that preserves key Kerr thermodynamic relations despite non-asymptotically flat boundaries.
-
Magnetic reconnection in five-dimensional Kerr black hole
Magnetic reconnection enables higher energy extraction efficiency from singly-rotating five-dimensional Kerr black holes than from doubly-rotating ones and can exceed the Blandford-Znajek process in the single-rotation case.
-
A Complete Invariant Analysis of the Kerr Spacetime and its Photon Region
An invariant function is derived whose zeros identify spherical photon orbits in Kerr spacetime, parameterized by an inclination angle, enabling invariant characterization of the photon region and constants of motion.
-
Shadow dependent phenomenology framework for rotating black hole metric
A thermodynamic-optical duality reparameterizes black hole mass via observable shadow radius to derive lensing angles, Hawking temperature, and luminosity for Kerr, Kerr-MOG, and rotating Horndeski metrics, yielding m...
-
Reshaping the inner shadow of a Kerr black hole by a torn accretion disk
Torn accretion disks around Kerr black holes erode the inner shadow and create bifurcated, crescent, and multi-ring shadow features driven by sub-disk discontinuities and outer tilt angle.
-
Photon rings and shadows of black holes with non-minimal couplings between curvature and electromagnetic field
Three distinct non-minimal curvature-EM couplings produce different enlargements or reductions of black hole shadows and alter photon ring separations in characteristic ways.
-
Relative Magnification Factor of Point Sources on Accretion Disks
Corotating point sources on accretion disks near black holes distort the relative magnification factor distribution, modulating caustics and encoding accretion flow kinematics via time-delayed images.
-
Gravity/thermodynamics correspondence via black hole shadows
Cuspy black hole shadows correspond to swallowtail thermodynamic free energy, with boundary self-intersections marking geometric phase transitions whose critical exponents fall in the mean-field class.
-
Superradiant Suppression of Non-minimally Coupled Scalar fields for a Rotating Charged dS Black Hole in Conformal Weyl Gravity
Superradiant amplification of charged scalar fields around rotating charged de Sitter black holes is suppressed in conformal Weyl gravity relative to general relativity, with strong exponential suppression for massive...
-
Quasinormal modes of massless scalar and electromagnetic perturbations for Euler Heisenberg black holes surrounded by perfect fluid dark matter
Quasinormal frequencies and greybody factors for massless scalar and electromagnetic perturbations in Euler-Heisenberg black holes with perfect fluid dark matter are calculated via AIM and sixth-order WKB, showing tha...
-
Jet-driven shocks and turbulence in radio-loud Active Galactic Nuclei observed with JWST MIRI/MRS
JWST spectroscopy reveals radio jets in nearby AGN drive multiphase ISM turbulence and shock-dominated H2 excitation both along and perpendicular to the jet direction.
-
The properties and predictions of quasi-periodic oscillations around a black hole in nonlocal gravity
Nonlocal gravity shrinks the ISCO radius, boosts QPO frequencies, and constrains α/M ≤ 0.452 with M ≲ 43.6 M_⊙ for observed high-frequency QPOs under resonance models.
-
Photon Surfaces in Higher-Curvature Gravity: Implications for Quasinormal Modes and Gravitational Lensing
Higher-curvature EFT terms modify the photon sphere radius, critical impact parameter, and strong deflection coefficients, providing sensitive probes for constraints on quantum gravity effects via lensing and QNM spectra.
-
Effective null geodesics and black hole images in Kruglov nonlinear electrodynamics
In Kruglov's Born-Infeld-type nonlinear electrodynamics, the effective photon geometry around a charged black hole produces q-dependent shifts in light deflection, shadow radius, and accretion disk images, including s...
-
Effective null geodesics and black hole images in Kruglov nonlinear electrodynamics
In Kruglov nonlinear electrodynamics, small positive values of the parameter q produce stable photon orbits outside the event horizon and modify black hole shadows and relativistic images even when the spacetime metri...
-
Regular Black Holes in General Relativity from Nonlinear Electrodynamics with de Sitter Cores
New regular black hole metrics in GR arise from a magnetic monopole NLED configuration with de Sitter cores, are fitted to Sgr A* shadow size, and remain stable under scalar perturbations.
-
Macroscopic Optical Nonreciprocity: A Black Hole as an Optical Diode
Rotating black holes with a nonminimally coupled Lorentz-violating background act as optical diodes by producing direction-dependent shadows that morph from quasi-symmetric to teardrop upon path reversal.
-
Scalarizations of magnetized Reissner-Nordstr\"om black holes induced by parity-violating and parity-preserving interactions
Magnetic fields lower the scalarization threshold for electromagnetic and gravitational Chern-Simons couplings but produce opposite trends on the two Gauss-Bonnet branches, with nonlinear terms converting exponential ...
-
Topologically equivalent yet radiatively distinct orbits in EMRI system
In dyonic black holes, periodic orbits with identical rotation numbers but spanning different curvature regions generate radiatively distinct gravitational waveforms in EMRIs.
-
Observational constraints on nonlocal black holes via gravitational lensing
Nonlocal black holes remain consistent with general relativity at the 1.13-sigma level after joint lensing and quasinormal-mode constraints.
-
Spectroscopy of analogue black holes using simulation-based inference
Simulation-based inference reliably extracts physical parameters from noisy spectra of analogue black holes.
-
Black Hole-Boson Star Binaries: Gravitational Wave Signals and Tidal Disruption
Numerical simulations of black hole-boson star binaries show that scalar self-interactions can suppress tidal disruption while radiative efficiency depends on the chosen potential.
-
Dynamical Black Hole Thermodynamics in Modified Gravity
In modified gravity, dynamical Schwarzschild black holes under scalar waves exhibit non-thermal particle creation while preserving the generalized second law and forming stable zero-temperature remnants at the extremal bound.
-
Cosmological coupled black holes immersed in dark sector
Exact solution for a black hole whose mass co-evolves with Hubble expansion via radius-dependent coupling to an anisotropic dark halo in FLRW spacetime.
-
Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
No evidence for deviations from general relativity is found in LIGO-Virgo binary black hole events, with improved constraints on waveform parameters, graviton mass, and ringdown properties.
-
Thin Accretion Disks around Rotating Charged Black Holes in an Effective Higher-Curvature Spacetime
An effective Gauss-Bonnet-like deformation of the Kerr-Newman metric moves the ISCO inward, raises radiative efficiency, flux, and temperature, while charge suppresses these quantities.
-
Optical Appearance of the Kerr-Bertotti-Robinson Black Hole with a Magnetically Driven Synchrotron Emissivity Model
Kerr-BR black hole images with magnetically coupled synchrotron emissivity show spin- and B-dependent shifts in the inner disk edge, altered lensing rings, and Doppler asymmetries, with retrograde cases displaying wid...
-
Probing Gravitational Wave Signatures from Periodic Orbits of Regular Black Holes in Asymptotically Safe Gravity
The quantum parameter ξ in an asymptotically safe regular black hole shifts the innermost stable orbit, enhances whirl behavior in periodic geodesics, and produces amplitude-modulated millihertz gravitational-wave str...
-
Jet-driven shocks and turbulence in radio-loud Active Galactic Nuclei observed with JWST MIRI/MRS
Radio jets drive shocks and turbulence in multiphase gas of nearby radio-loud AGN as mapped by JWST spectroscopy.
-
Thermodynamics and orbital structure of anti-de Sitter black holes in Palatini-inspired nonlinear electrodynamics
An exact AdS extension of the PINLED black hole is derived from the Einstein-Hilbert action plus nonlinear EM sector, preserving the original parametric form while adding the standard AdS lapse term, followed by full ...
-
Photon Sphere and Shadow of a Perturbative Black Hole in $f(R,\mathcal{G})$ Gravity
Perturbative higher-curvature corrections in f(R,G) gravity shift the photon-sphere radius and black-hole shadow size away from Schwarzschild values, with the Gauss-Bonnet sector contributing more than mixed terms.
-
Probing Kalb-Ramond gravity with charged rotating black holes: constraints from EHT observations
EHT shadow observations constrain the Lorentz-violating parameter ℓ in Kalb-Ramond gravity for charged rotating black holes to roughly |ℓ| ≲ 0.1-0.2, with an upper bound ℓ ≲ 0.19 from Sgr A*.
-
Review of strongly coupled regimes in gravity with Dyson-Schwinger approach
Dyson-Schwinger methods applied to gravity theories produce conformally flat metrics and a sequence of cosmological phase transitions from conformal symmetry breaking that non-minimal scalar couplings can suppress.
-
Polarization Signatures from GRMHD Simulations of Black Hole Accretion
Polarization signatures from GRMHD simulations of black hole accretion can help probe disk, corona, and jet properties when combined with X-ray polarimetry observations.
Reference graph
Works this paper leans on
-
[1]
Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2016, PhRvL, 116, 061102
work page 2016
-
[2]
Abramowski, A., Acero, F., Aharonian, F., et al. 2012, ApJ, 746, 151
work page 2012
- [3]
- [4]
- [5]
- [6]
-
[7]
Peters, W. L. 1999, PASP, 111, 627
work page 1999
- [8]
-
[9]
Balick, B., & Brown, R. L. 1974, ApJ, 194, 265
work page 1974
- [10]
- [11]
-
[12]
Barausse, E., & Sotiriou, T. P. 2008, PhRvL, 101, 099001
work page 2008
-
[13]
Bardeen, J. M. 1973, in Black Holes, ed. C. DeWitt & B. S. DeWitt (New York: Gordon and Breach ), 215
work page 1973
-
[14]
Berti, E., Barausse, E., Cardoso, V., et al. 2015, CQGra, 32, 243001
work page 2015
-
[15]
Bird, S., Harris, W. E., Blakeslee, J. P., & Flynn, C. 2010, A&A, 524, A71
work page 2010
- [16]
- [17]
-
[18]
P., Jordán, A., Mei, S., et al
Blakeslee, J. P., Jordán, A., Mei, S., et al. 2009, ApJ, 694, 556
work page 2009
- [19]
- [20]
- [21]
- [22]
-
[23]
Blecher, T., Deane, R., Bernardi, G., & Smirnov, O. 2017, MNRAS, 464, 143
work page 2017
-
[24]
Boccardi, B., Krichbaum, T. P., Ros, E., & Zensus, J. A. 2017, A&ARv, 25, 4
work page 2017
- [25]
-
[26]
Bouman, K. L., Johnson, M. D., Dalca, A. V., et al. 2018, IEEE Transactions on Computational Imaging , 4, 512
work page 2018
-
[27]
Bouman, K. L., Johnson, M. D., Zoran, D., et al. 2016, in The IEEE Conf. Computer Vision and Pattern Recognition (New York: IEEE ), 913
work page 2016
-
[28]
Bower, G. C., Wright, M. C. H., Falcke, H., & Backer, D. C. 2003, ApJ, 588, 331
work page 2003
- [29]
-
[30]
E., Johannsen, T., Loeb, A., & Psaltis, D
Broderick, A. E., Johannsen, T., Loeb, A., & Psaltis, D. 2014, ApJ, 784, 7
work page 2014
- [31]
- [32]
- [33]
- [34]
-
[35]
E., Narayan, R., Kormendy, J., et al
Broderick, A. E., Narayan, R., Kormendy, J., et al. 2015, ApJ, 805, 179
work page 2015
- [36]
-
[37]
Bronzwaer, T., Davelaar, J., Younsi, Z., et al. 2018, A&A, 613, A2
work page 2018
-
[38]
Cantiello, M., Blakeslee, J. P., Ferrarese, L., et al. 2018, ApJ, 856, 126
work page 2018
-
[39]
Chael, A., Narayan, R., & Johnson, M. D. 2018a, arXiv: 1810.01983
-
[40]
Chan, C.-K., Psaltis, D., Özel, F., Narayan, R., & Saowski, A. 2015, ApJ, 799, 1
work page 2015
-
[41]
Chirenti, C. B. M. H., & Rezzolla, L. 2007, CQGra, 24, 4191
work page 2007
-
[42]
Clark, B. G. 1980, A&A, 89, 377
work page 1980
- [43]
-
[44]
Cunha, P. V. P., Grover, J., Herdeiro, C., et al. 2016, PhRvD, 94, 104023
work page 2016
-
[45]
Curtis, H. D. 1918, PLicO, 13, 9
work page 1918
-
[46]
2019, A&A, submitted de Gasperin, F., Orrú, E., Murgia, M., et al
Davelaar, J., Olivares, H., Porth, O., et al. 2019, A&A, submitted de Gasperin, F., Orrú, E., Murgia, M., et al. 2012, A&A, 547, A56
work page 2019
-
[47]
Deller, A. T., Tingay, S. J., Bailes, M., & West, C. 2007, PASP, 119, 318
work page 2007
- [48]
-
[49]
Dibi, S., Drappeau, S., Fragile, P. C., Markoff, S., & Dexter, J. 2012, MNRAS, 426, 1928
work page 2012
-
[50]
2009a, astro2010: The Astronomy and Astrophysics Decadal Survey, Vol
Doeleman, S., Agol, E., Dacker, D., et al. 2009a, astro2010: The Astronomy and Astrophysics Decadal Survey, Vol. 2010
work page 2010
- [51]
-
[52]
Doeleman, S. S., Shen, Z.-Q., Rogers, A. E. E., et al. 2001, AJ, 121, 2610
work page 2001
-
[53]
Doeleman, S. S., Weintroub, J., Rogers, A. E. E., et al. 2008, Natur, 455, 78
work page 2008
-
[54]
1997, MNRAS, 284, 576 EHT Collaboration et al
Eckart, A., & Genzel, R. 1997, MNRAS, 284, 576 EHT Collaboration et al. 2019a, ApJL, 875, L2 (Paper II ) EHT Collaboration et al. 2019b, ApJL, 875, L3 (Paper III ) EHT Collaboration et al. 2019c, ApJL, 875, L4 (Paper IV ) EHT Collaboration et al. 2019d, ApJL, 875, L5 (Paper V ) EHT Collaboration et al. 2019e, ApJL, 875, L6 (Paper VI )
work page 1997
-
[55]
Einstein, A. 1915, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin: Deutsche Akademie der Wissenschaften zu Berlin )
work page 1915
- [56]
-
[57]
Falcke, H., Mannheim, K., & Biermann, P. L. 1993, A&A, 278, L1
work page 1993
-
[58]
2019, AdSpR, in press (arXiv:1903.09539)
Fish, V., Shea, M., & Akiyama, K. 2019, AdSpR, in press (arXiv:1903.09539)
-
[59]
Fish, V. L., Johnson, M. D., Doeleman, S. S., et al. 2016, ApJ, 820, 90
work page 2016
-
[60]
Ford, H. C., Harms, R. J., Tsvetanov, Z. I., et al. 1994, ApJL, 435, L27
work page 1994
- [61]
-
[62]
Gebhardt, K., Adams, J., Richstone, D., et al. 2011, ApJ, 729, 119
work page 2011
- [63]
-
[64]
Ghez, A. M., Klein, B. L., Morris, M., & Becklin, E. E. 1998, ApJ, 509, 678
work page 1998
-
[65]
Giddings, S. B. 2017, NatAs, 1, 0067
work page 2017
-
[66]
Goddi, C., Marti-Vidal, I., Messias, H., et al. 2019, PASP, in press
work page 2019
-
[67]
2019, ApJS Gravity Collaboration, Abuter, R., Amorim, A., et al
Gold, R., Broderick, A., Younsi, Z., et al. 2019, ApJS Gravity Collaboration, Abuter, R., Amorim, A., et al. 2018a, A&A, 615, L15 Gravity Collaboration, Abuter, R., Amorim, A., et al. 2018b, A&A, 618, L10
work page 2019
-
[68]
Greisen, E. W. 2003, in Information Handling in Astronomy —Historical
work page 2003
-
[69]
Grenzebach, A., Perlick, V., & Lämmerzahl, C. 2014, PhRvD, 89, 124004
work page 2014
- [70]
- [71]
- [72]
- [73]
- [74]
-
[75]
Hawking, S. W. 1976, PhRvD, 14, 2460
work page 1976
-
[76]
Hilbert, D. 1917, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen —Mathematisch-physikalische Klasse (Berlin: Weidmannsche Buchhandlung )
work page 1917
-
[77]
Ho, L. C. 1999, ApJ, 516, 672 Högbom, J. A. 1974, A&AS, 15, 417
work page 1999
-
[78]
Honma, M., Akiyama, K., Uemura, M., & Ikeda, S. 2014, PASJ, 66, 95
work page 2014
- [79]
- [80]
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.