Our Galactic Centre, Sagittarius A*, is believed to harbour a supermassive black hole, as suggested by observations tracking individual orbiting stars1,2. Upcoming submillimetre very-long baseline interferometry images of Sagittarius A* carried out by the Event Horizon Telescope collaboration (EHTC)3,4 are expected to provide critical evidence for the existence of this supermassive black hole5,6. We assess our present ability to use EHTC images to determine whether they correspond to a Kerr black hole as predicted by Einstein’s theory of general relativity or to a black hole in alternative theories of gravity. To this end, we perform general-relativistic magnetohydrodynamical simulations and use general-relativistic radiative-transfer calculations to generate synthetic shadow images of a magnetized accretion flow onto a Kerr black hole. In addition, we perform these simulations and calculations for a dilaton black hole, which we take as a representative solution of an alternative theory of gravity. Adopting the very-long baseline interferometry configuration from the 2017 EHTC campaign, we find that it could be extremely difficult to distinguish between black holes from different theories of gravity, thus highlighting that great caution is needed when interpreting black hole images as tests of general relativity.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Journal of High Energy Physics Open Access 15 September 2022
Experimental Astronomy Open Access 27 May 2021
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$119.00 per year
only $9.92 per issue
Rent or buy this article
Prices vary by article type
Prices may be subject to local taxes which are calculated during checkout
Eckart, A. & Genzel, R. Observations of stellar proper motions near the Galactic Centre. Nature 383, 415–417 (1996).
Genzel, R., Eisenhauer, F. & Gillessen, S. The Galactic Center massive black hole and nuclear star cluster. Rev. Mod. Phys. 82, 3121–3195 (2010).
Doeleman, S. S. et al. Event-horizon–scale structure in the supermassive black hole candidate at the Galactic Centre. Nature 455, 78–80 (2008).
Goddi, C. et al. BlackHoleCam: fundamental physics of the Galactic Center. Int. J. Mod. Phys. D 26, 1730001–1730239 (2017).
Broderick, A. E., Johannsen, T., Loeb, A. & Psaltis, D. Testing the no-hair theorem with Event Horizon Telescope observations of Sagittarius A*. Astrophys. J. 784, 7 (2014).
Johannsen, T. Testing the no-hair theorem with observations of black holes in the electromagnetic spectrum. Class. Quant. Grav. 33, 124001 (2016).
Cunningham, C. T. & Bardeen, J. M. The optical appearance of a star orbiting an extreme Kerr black hole. Astrophys. J. 183, 237–264 (1973).
Luminet, J.-P. Image of a spherical black hole with thin accretion disk. Astron. Astrophys. 75, 228–235 (1979).
Falcke, H., Melia, F. & Agol, E. Viewing the shadow of the black hole at the Galactic Center. Astrophys. J. Lett. 528, L13–L16 (2000).
Dexter, J., Agol, E. & Fragile, P. C. Millimeter flares and VLBI visibilities from relativistic simulations of magnetized accretion onto the Galactic Center black hole. Astrophys. J. Lett. 703, L142–L146 (2009).
Mościbrodzka, M., Falcke, H., Shiokawa, H. & Gammie, C. F. Observational appearance of inefficient accretion flows and jets in 3D GRMHD simulations: application to Sagittarius A*. Astron. Astrophys. 570, A7 (2014).
Chan, C.-K., Psaltis, D., Özel, F., Narayan, R. & Sadowski, A. The power of imaging: constraining the plasma properties of GRMHD simulations using EHT observations of Sgr A*. Astrophys. J. 799, 1 (2015).
Gold, R., McKinney, J. C., Johnson, M. D. & Doeleman, S. S. Probing the magnetic field structure in Sgr A* on black hole horizon scales with polarized radiative transfer simulations. Astrophys. J. 837, 180 (2017).
Porth, O. et al. The black hole accretion code. Comput. Astrophys. Cosmol. 4, 1 (2017).
Rezzolla, L. & Zhidenko, A. New parametrization for spherically symmetric black holes in metric theories of gravity. Phys. Rev. D 90, 084009 (2014).
Broderick, A. E., Fish, V. L., Doeleman, S. S. & Loeb, A. Evidence for low black hole spin and physically motivated accretion models from millimeter-VLBI observations of Sagittarius A*. Astrophys. J. 735, 110 (2011).
Broderick, A. E. et al. Modeling seven years of Event Horizon Telescope observations with radiatively inefficient accretion flow models. Astrophys. J. 820, 137 (2016).
Garca, A., Galtsov, D. & Kechkin, O. Class of stationary axisymmetric solutions of the Einstein–Maxwell-dilaton–axion field equations. Phys. Rev. Lett. 74, 1276–1279 (1995).
Damour, T. & Polyakov, A. M. The string dilation and a least coupling principle. Nucl. Phys. B 423, 532–558 (1994).
Gammie, C. F., McKinney, J. C. & Tóth, G. Harm: a numerical scheme for general relativistic magnetohydrodynamics. Astrophys. J. 589, 458 (2003).
Mościbrodzka, M. & Falcke, H. Coupled jet-disk model for Sagittarius A*: explaining the flat-spectrum radio core with GRMHD simulations of jets. Astron. Astrophys. 559, L3 (2013).
Younsi, Z., Zhidenko, A., Rezzolla, L., Konoplya, R. & Mizuno, Y. New method for shadow calculations: application to parametrized axisymmetric black holes. Phys. Rev. D. 94, 084025 (2016).
Buscher, D. F. Direct maximum-entropy image reconstruction from the bispectrum. IAU Symp. P. Ser. 158, 91 (1994).
Chael, A. A. et al. High-resolution linear polarimetric imaging for the Event Horizon Telescope. Astrophys. J. 829, 11 (2016).
Lu, R.-S. et al. Imaging an event horizon: mitigation of source variability of Sagittarius A*. Astrophys. J. 817, 173 (2016).
Dexter, J. & O’Leary, R. M. The peculiar pulsar population of the central parsec. Astrophys. J. Lett. 783, L7 (2014).
Psaltis, D., Wex, N. & Kramer, M. A quantitative test of the no-hair theorem with Sgr A* using stars, pulsars, and the Event Horizon Telescope. Astrophys. J. 818, 121 (2016).
Meliani, Z. et al. Simulations of recoiling black holes: adaptive mesh refinement and radiative transfer. Astron. Astrophys. 598, A38 (2017).
Font, J. A. & Daigne, F. On the stability of thick accretion disks around black holes. Astrophys. J. 581, L23–L26 (2002).
Rezzolla, L. & Zanotti, O. Relativistic Hydrodynamics (Oxford Univ. Press, Oxford, 2013).
Konoplya, R., Rezzolla, L. & Zhidenko, A. General parametrization of axisymmetric black holes in metric theories of gravity. Phys. Rev. D 93, 064015 (2016).
Johannsen, T. & Psaltis, D. Metric for rapidly spinning black holes suitable for strong-field tests of the no-hair theorem. Phys. Rev. D 83, 124015 (2011).
De Laurentis, M., Younsi, Z., Porth, O., Mizuno, Y. & Rezzolla, L. Test-particle dynamics in general spherically symmetric black hole spacetimes. Preprint at https://arxiv.org/abs/1712.00265 (2017).
Shiokawa, H., Dolence, J. C., Gammie, C. F. & Noble, S. C. Global general relativistic magnetohydrodynamic simulations of black hole accretion flows: a convergence study. Astrophys. J. 744, 187 (2012).
Younsi, Z., Wu, K. & Fuerst, S. V. General relativistic radiative transfer: formulation and emission from structured tori around black holes. Astron. Astrophys. 545, A13 (2012).
Boehle, A. et al. An improved distance and mass estimate for Sgr A* from a multistar orbit analysis. Astrophys. J. 830, 17 (2016).
Mościbrodzka, M., Gammie, C. F., Dolence, J. C., Shiokawa, H. & Leung, P. K. Radiative models of Sgr A* from GRMHD simulations. Astrophys. J. 706, 497–507 (2009).
Psaltis, D. et al. Event Horizon Telescope evidence for alignment of the black hole in the center of the Milky Way with the inner stellar disk. Astrophys. J. 798, 15 (2015).
Marrone, D. P., Moran, J. M., Zhao, J.-H. & Rao, R. Interferometric measurements of variable 340 GHz linear polarization in Sagittarius A*. Astrophys. J. 640, 308–318 (2006).
Doeleman, S. S., Fish, V. L., Broderick, A. E., Loeb, A. & Rogers, A. E. E. Detecting flaring structures in Sagittarius A* with high-frequency VLBI. Astrophys. J. 695, 59–74 (2009).
Lu, R.-S. et al. Imaging the supermassive black hole shadow and jet base of M87 with the Event Horizon Telescope. Astrophys. J. 788, 120 (2014).
Högbom, J. A. Aperture synthesis with a non-regular distribution of interferometer baselines. Astron. Astrophys. Supp. 15, 417 (1974).
Wang, Z., Bovik, A. C., Sheikh, H. R. & Simoncelli, E. P. Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13, 600–612 (2004).
We thank M. Moscibrodzka, T. Bronzwaer and J. Davelaar for fruitful discussions. This research is supported by the ERC synergy grant ‘BlackHoleCam: Imaging the Event Horizon of Black Holes’ (grant number 610058). Z.Y. acknowledges support from an Alexander von Humboldt Fellowship. H.O. is supported in part by a CONACYT-DAAD scholarship. The simulations were performed on LOEWE at the CSC-Frankfurt and Iboga at ITP Frankfurt.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Mizuno, Y., Younsi, Z., Fromm, C.M. et al. The current ability to test theories of gravity with black hole shadows. Nat Astron 2, 585–590 (2018). https://doi.org/10.1038/s41550-018-0449-5
This article is cited by
General Relativity and Gravitation (2023)
Science China Physics, Mechanics & Astronomy (2023)
Journal of High Energy Physics (2022)
Science China Physics, Mechanics & Astronomy (2022)
Nature Astronomy (2021)