Schwarzschild, K. On the gravitational field of a mass point according to Einstein’s theory. Abh. Konigl. Preuss. Akad. Wiss. Berlin 1916, 189–196 (1916).
Google Scholar
Kerr, R. P. Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11, 237–238 (1963). An exact analytical solution of general relativity describing the most general spinning uncharged black hole.
Google Scholar
Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (Princeton Univ. Press, 2018).
Michell, J. On the means of discovering the distance, magnitude, &c. of the fixed stars, in consequence of the diminution of the velocity of their light, in case such a diminution should be found to take place in any of them, and such other data should be procured from observations, as would be farther necessary for that purpose. By the Rev. John Michell, B. D. F. R. S. in a letter to Henry Cavendish, Esq. F. R. S. and A. S. Phil. Trans. R. Soc. Lond. 74, 35–57 (1784).
Laplace, P. S. Beweis des Satzes, dass die anziehende Kraft bey einem Weltkörper so groß seyn könne, dass das Licht davon nicht ausströmen kann. Allg. Geogr. Ephemer. 4, 1–6 (1799).
Thorne, K. S. Black Holes and Time Warps: Einstein’s Outrageous Legacy (W. W. Norton, 1994).
Begelman, M. & Rees, M. Gravity’s Fatal Attraction (Cambridge Univ. Press, 2020).
Penrose, R. Gravitational collapse and space-time singularities. Phys. Rev. Lett. 14, 57–59 (1965). Mathematical proof that black-hole formation is inevitable in general relativity from certain generic initial conditions.
Google Scholar
Hawking, S. W. Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975).
Google Scholar
Schmidt, M. 3C 273 : a star-like object with large red-shift. Nature 197, 1040 (1963). Discovery that the quasar 3C 273, later identified as an accreting supermassive black hole, is at a redshift of 0.158 and therefore very distant from our Galaxy and highly luminous.
Google Scholar
Salpeter, E. E. Accretion of interstellar matter by massive objects. Astrophys. J. 140, 796–800 (1964).
Google Scholar
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, 13–16 (2000).
Google Scholar
Event Horizon Telescope Collaboration First M87 Event Horizon Telescope results. I. The shadow of the supermassive black hole. Astrophys. J. Lett. 875, 1 (2019). Landmark experiment with the Event Horizon Telescope that obtained the image of the supermassive black hole M87* and confirmed the predicted black-hole shadow.
Google Scholar
Event Horizon Telescope Collaboration First Sagittarius A* Event Horizon Telescope results. I. The shadow of the supermassive black hole in the center of the Milky Way. Astrophys. J. Lett. 930, 12 (2022).
Google Scholar
Eckart, A. & Genzel, R. Observations of stellar proper motions near the Galactic Centre. Nature 383, 415–417 (1996).
Google Scholar
Ghez, A. M., Klein, B. L., Morris, M. & Becklin, E. E. High proper-motion stars in the vicinity of Sagittarius A*: evidence for a supermassive black hole at the center of our Galaxy. Astrophys. J. 509, 678–686 (1998).
Google Scholar
Ghez, A. M., Morris, M., Becklin, E. E., Tanner, A. & Kremenek, T. The accelerations of stars orbiting the Milky Way’s central black hole. Nature 407, 349–351 (2000). Measurement of the accelerations of stars orbiting the object Sagittarius A* at the centre of the Galaxy.
Google Scholar
Schödel, R. et al. A star in a 15.2-year orbit around the supermassive black hole at the centre of the Milky Way. Nature 419, 694–696 (2002). Landmark study that reported a nearly complete orbit of a star at the centre of our Galaxy and proved beyond reasonable doubt that Sagittarius A* is a four-million-solar-mass black hole.
Google Scholar
Ghez, A. M. et al. Stellar orbits around the Galactic Center black hole. Astrophys. J. 620, 744–757 (2005).
Google Scholar
Gebhardt, K. et al. The Black Hole mass in M87 from Gemini/NIFS adaptive optics observations. Astrophys. J. 729, 119 (2011).
Hees, A. et al. Testing general relativity with stellar orbits around the supermassive black hole in our Galactic Center. Phys. Rev. Lett. 118, 211101 (2017).
Google Scholar
GRAVITY Collaboration Detection of the gravitational redshift in the orbit of the star S2 near the Galactic Centre massive black hole. Astron. Astrophys. 615, 15 (2018).
Google Scholar
Do, T. et al. Relativistic redshift of the star S0-2 orbiting the Galactic Center supermassive black hole. Science 365, 664–668 (2019).
Google Scholar
GRAVITY Collaboration Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic Centre massive black hole. Astron. Astrophys. 636, 5 (2020).
Google Scholar
Di Matteo, T., Springel, V. & Hernquist, L. Energy input from quasars regulates the growth and activity of black holes and their host galaxies. Nature 433, 604–607 (2005).
Google Scholar
Brüggen, M. & Kaiser, C. R. Hot bubbles from active galactic nuclei as a heat source in cooling-flow clusters. Nature 418, 301–303 (2002).
Google Scholar
Cattaneo, A. et al. The role of black holes in galaxy formation and evolution. Nature 460, 213–219 (2009).
Google Scholar
Fabian, A. C. Observational evidence of active galactic nuclei feedback. Annu. Rev. Astron. Astrophys. 50, 455–489 (2012).
Google Scholar
Balbus, S. A. & Hawley, J. F. A powerful local shear instability in weakly magnetized disks. I. Linear analysis. Astrophys. J. 376, 214–222 (1991).
Google Scholar
Shakura, N. I. & Sunyaev, R. A. Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355 (1973).
Novikov, I. D. & Thorne, K. S. in Black Holes (Les Astres Occlus) (eds DeWitt, C. & DeWitt, B.) 343–450 (Gordon & Breach, 1973).
Esin, A. A., McClintock, J. E. & Narayan, R. Advection-dominated accretion and the spectral states of black hole X-ray binaries: application to Nova Muscae 1991. Astrophys. J. 489, 865–889 (1997).
Google Scholar
Fabian, A. C. & Canizares, C. R. Do massive black holes reside in elliptical galaxies? Nature 333, 829–831 (1988).
Google Scholar
Ho, L. C. Nuclear activity in nearby galaxies. Ann. Rev. Astron. Astrophys. 46, 475–539 (2008).
Google Scholar
Goldwurm, A. et al. Possible evidence against a massive black hole at the Galactic Centre. Nature 371, 589–591 (1994).
Google Scholar
Grindlay, J. E. Black holes take centre stage? Nature 371, 561–562 (1994).
Google Scholar
Krichbaum, T. P. et al. VLBI observations of the Galactic Center source SGR A* at 86 GHz and 215 GHz. Astron. Astrophys. 335, 106–110 (1998).
Shen, Z.-Q., Lo, K. Y., Liang, M. C., Ho, P. T. P. & Zhao, J.-H. A size of ~1 au for the radio source Sgr A* at the centre of the Milky Way. Nature 438, 62–64 (2005).
Google Scholar
Yuan, F. & Narayan, R. Hot accretion flows around black holes. Ann. Rev. Astron. Astrophys. 52, 529–588 (2014).
Google Scholar
Shapiro, S. L., Lightman, A. P. & Eardley, D. M. A two-temperature accretion disk model for Cygnus X-1: structure and spectrum. Astrophys. J. 204, 187–199 (1976).
Google Scholar
Pringle, J. E. Thermal instabilities in accretion discs. Mon. Not. R. Astron. Soc. 177, 65–71 (1976).
Google Scholar
Piran, T. The role of viscosity and cooling mechanisms in the stability of accretion disks. Astrophys. J. 221, 652–660 (1978).
Google Scholar
Ichimaru, S. Bimodal behavior of accretion disks: theory and application to Cygnus X-1 transitions. Astrophys. J. 214, 840–855 (1977).
Google Scholar
Rees, M. J., Begelman, M. C., Blandford, R. D. & Phinney, E. S. Ion-supported tori and the origin of radio jets. Nature 295, 17–21 (1982).
Google Scholar
Narayan, R. & Yi, I. Advection-dominated accretion: a self-similar solution. Astrophys. J. Lett. 428, 13–16 (1994).
Google Scholar
Narayan, R. & Yi, I. Advection-dominated accretion: underfed black holes and neutron stars. Astrophys. J. 452, 710–735 (1995).
Google Scholar
Abramowicz, M. A., Chen, X., Kato, S., Lasota, J.-P. & Regev, O. Thermal equilibria of accretion disks. Astrophys. J. Lett. 438, 37–39 (1995).
Google Scholar
Narayan, R., Mahadevan, R. & Quataert, E. in Theory of Black Hole Accretion Disks (eds Abramowicz, M. A. et al.) 148–182 (Cambridge Univ. Press, 1998).
Narayan, R., Yi, I. & Mahadevan, R. Explaining the spectrum of Sagittarius A* with a model of an accreting black hole. Nature 374, 623–625 (1995). Application of the hot-accretion-flow model to an astrophysical black hole, Sagittarius A* at our Galactic Centre.
Google Scholar
Reynolds, C. S., Di Matteo, T., Fabian, A. C., Hwang, U. & Canizares, C. R. The ‘quiescent’ black hole in M87. Mon. Not. R. Astron. Soc. 283, 111–116 (1996).
Google Scholar
Thompson, A. R., Moran, J. M. & Swenson, G. W. Interferometry and Synthesis in Radio Astronomy 3rd edn (Springer, 2017).
Eisenhauer, F. et al. GRAVITY: getting to the event horizon of Sgr A*. In Optical and Infrared Interferometry Society of Photo-Optical Instrumentation Engineers Conference Series Vol. 7013 (eds Schöller, M. et al.) 70132 (SPIE, 2008).
Walker, R. C., Hardee, P. E., Davies, F. B., Ly, C. & Junor, W. The structure and dynamics of the subparsec jet in M87 based on 50 VLBA observations over 17 Years at 43 GHz. Astrophys. J. 855, 128 (2018).
Baganoff, F. K. et al. Rapid X-ray flaring from the direction of the supermassive black hole at the Galactic Centre. Nature 413, 45–48 (2001).
Google Scholar
Genzel, R. et al. Near-infrared flares from accreting gas around the supermassive black hole at the Galactic Centre. Nature 425, 934–937 (2003).
Google Scholar
Ghez, A. M. et al. Variable infrared emission from the supermassive black hole at the center of the Milky Way. Astrophys. J. Lett. 601, 159–162 (2004).
Google Scholar
GRAVITY Collaboration Detection of orbital motions near the last stable circular orbit of the massive black hole SgrA*. Astron. Astrophys. 618, 10 (2018). Detection of looped clockwise motion of infrared-emitting gas around the Galactic Centre black hole Sagittarius A*.
Google Scholar
Gammie, C. F., McKinney, J. C. & Tóth, G. HARM: a numerical scheme for general relativistic magnetohydrodynamics. Astrophys. J. 589, 444–457 (2003).
Google Scholar
De Villiers, J.-P. & Hawley, J. F. A numerical method for general relativistic magnetohydrodynamics. Astrophys. J. 589, 458–480 (2003).
Google Scholar
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).
Google Scholar
Dexter, J., Agol, E., Fragile, P. C. & McKinney, J. C. The submillimeter bump in Sgr A* from relativistic MHD simulations. Astrophys. J. 717, 1092–1104 (2010).
Google Scholar
Event Horizon Telescope Collaboration First Sagittarius A* Event Horizon Telescope results. V. Testing astrophysical models of the Galactic Center black hole. Astrophys. J. Lett. 930, 16 (2022).
Google Scholar
Event Horizon Telescope Collaboration First M87 Event Horizon Telescope results. VIII. Magnetic field structure near the event horizon. Astrophys. J. Lett. 910, 13 (2021).
Google Scholar
Agol, E. Sagittarius A* polarization: no advection-dominated accretion flow, low accretion rate, and nonthermal synchrotron emission. Astrophys. J. Lett. 538, 121–124 (2000).
Google Scholar
Quataert, E. & Gruzinov, A. Constraining the accretion rate onto Sagittarius A* using linear polarization. Astrophys. J. 545, 842–846 (2000).
Google Scholar
Event Horizon Telescope Collaboration First Sagittarius A* Event Horizon Telescope results. VI. Testing the black hole metric. Astrophys. J. Lett. 930, 17 (2022).
Google Scholar
Newman, E. T. et al. Metric of a rotating, charged mass. J. Math. Phys. 6, 918–919 (1965).
Google Scholar
Blandford, R. D. & Znajek, R. L. Electromagnetic extraction of energy from Kerr black holes. Mon. Not. R. Astron. Soc. 179, 433–456 (1977). Demonstration that magnetic fields threading the black-hole horizon can extract rotational energy of the black hole, powering relativistic jets.
Google Scholar
Darwin, C. The gravity field of a particle. Proc. R. Soc. Lond. Ser. A 249, 180–194 (1959).
Bardeen, J. M. in Black Holes (Les Astres Occlus) (eds DeWitt, C. & DeWitt, B.) 241–289 (Gordon & Breach, 1973).
Johnson, M. D. & Lupsasca, A. et al. Universal interferometric signatures of a black hole’s photon ring. Sci. Adv. 6, 1310 (2020). Description of the formation of a set of nested self-similar subrings by black-hole lensing, and discussion of how the subrings could be disentangled in the image via interferometry.
Google Scholar
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).
Google Scholar
Psaltis, D. et al. Gravitational test beyond the first post-Newtonian order with the shadow of the M87 black hole. Phys. Rev. Lett. 125, 141104 (2020).
Google Scholar
Chael, A., Johnson, M. D. & Lupsasca, A. Observing the inner shadow of a black hole: a direct view of the event horizon. Astrophys. J. 918, 6 (2021).
Google Scholar
Johannsen, T. & Psaltis, D. Testing the no-hair theorem with observations in the electromagnetic spectrum. II. Black hole images. Astrophys. J. 718, 446–454 (2010).
Google Scholar
Gralla, S. E., Lupsasca, A. & Marrone, D. P. The shape of the black hole photon ring: a precise test of strong-field general relativity. Phys. Rev. D 102, 124004 (2020).
Google Scholar
Penrose, R. Gravitational collapse: the role of general relativity. Nuovo Cimento Rivista Serie 1, 252 (1969).
Bardeen, J. M., Press, W. H. & Teukolsky, S. A. Rotating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation. Astrophys. J. 178, 347–370 (1972).
Google Scholar
Semenov, V., Dyadechkin, S. & Punsly, B. Simulations of jets driven by black hole rotation. Science 305, 978–980 (2004).
Google Scholar
Tchekhovskoy, A., Narayan, R. & McKinney, J. C. Efficient generation of jets from magnetically arrested accretion on a rapidly spinning black hole. Mon. Not. R. Astron. Soc. 418, 79–83 (2011).
Google Scholar
Ricarte, A., Palumbo, D. C. M., Narayan, R., Roelofs, F. & Emami, R. Observational signatures of frame dragging in strong gravity. Astrophys. J. Lett. 941, L12 (2022).
Falcke, H. & Markoff, S. The jet model for Sgr A*: radio and X-ray spectrum. Astron. Astrophys. 362, 113–118 (2000).
Yusef-Zadeh, F., Roberts, D., Wardle, M., Heinke, C. O. & Bower, G. C. Flaring activity of Sagittarius A* at 43 and 22 GHz: evidence for expanding hot plasma. Astrophys. J. 650, 189–194 (2006).
Google Scholar
Brinkerink, C. D., Falcke, H., Law, C. J., Barkats, D. & Bower, G. C. et al. ALMA and VLA measurements of frequency-dependent time lags in Sagittarius A*: evidence for a relativistic outflow. Astron. Astrophys. 576, 41 (2015).
Google Scholar
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).
Google Scholar
Arzoumanian, Z. et al. The NANOGrav 12.5 yr data set: search for an isotropic stochastic gravitational-wave background. Astrophys. J. Lett. 905, 34 (2020).
Google Scholar
Kalogera, V. et al. The next generation global gravitational wave observatory: the science book. Preprint at https://arxiv.org/abs/2111.06990 (2021).
Amaro-Seoane, P. et al. Laser Interferometer Space Antenna. Preprint at https://arxiv.org/abs/1702.00786 (2017).
Chael, A. A. et al. Interferometric imaging directly with closure phases and closure amplitudes. Astrophys. J. 857, 23 (2018).
Google Scholar
Event Horizon Telescope Collaboration First M87 Event Horizon Telescope results. IV. Imaging the central supermassive black hole. Astrophys. J. Lett. 875, 4 (2019).
Google Scholar
Event Horizon Telescope Collaboration First M87 Event Horizon Telescope results. VII. Polarization of the ring. Astrophys. J. Lett. 910, 12 (2021).
Google Scholar
Event Horizon Telescope Collaboration First Sagittarius A* Event Horizon Telescope results. III. Imaging of the Galactic Center supermassive black hole. Astrophys. J. Lett. 930, 14 (2022).
Google Scholar
Goddi, C. et al. Polarimetric properties of Event Horizon Telescope targets from ALMA. Astrophys. J. Lett. 910, 14 (2021).
Google Scholar
Kravchenko, E. et al. Linear polarization in the nucleus of M87 at 7 mm and 1.3 cm. Astron. Astrophys. 637, 6 (2020).
Google Scholar
Owen, F. N., Eilek, J. A. & Kassim, N. E. M87 at 90 centimeters: a different picture. Astrophys. J. 543, 611–619 (2000).
Google Scholar