Difficulties of quantitative tests of the Kerr-hypothesis with X-ray observations of mass accreting black holes

  • Henric KrawczynskiEmail author
Editor’s Choice (Invited Review: State of the Field)
Part of the following topical collections:
  1. Testing the Kerr spacetime with gravitational-wave and electromagnetic observations


X-ray studies of stellar mass black holes in X-ray binaries and mass-accreting supermassive black holes in Active Galactic Nuclei have achieved a high degree of maturity and have delivered detailed information about the astrophysical sources and the physics of black hole accretion. In this article, I review recent progress made towards using the X-ray observations for testing the “Kerr hypothesis” that the background spacetimes of all astrophysical quasi-stationary black holes are described by the Kerr metric. Although the observations have indeed revealed clear evidence for relativistic effects in strong-field gravity, quantitative tests of the Kerr hypothesis still struggle with theoretical and practical difficulties. In this article, I describe several recently introduced test metrics and review the status of constraining the background spacetimes of mass accreting stellar mass and supermassive black holes with these test metrics. The main conclusion of the discussion is that astrophysical uncertainties are large compared to the rather small observational differences between the Kerr and non-Kerr metrics precluding quantitative constraints on deviations from the Kerr metric at this point in time. I conclude with discussing future progress enabled by more detailed numerical simulations and by future X-ray spectroscopy, timing, polarimetry, and interferometry missions.


General relativity Black holes No-hair theorem Kerr hypothesis Black hole spins 



I thank Q. Abarr, B. Beheshtipour, P. Bolt, M. Errando, C. Gammie, J. García, B. Groebe, A. Ingram, F. Kislat, and J. Miller for highly enjoyable and helpful discussions. I am grateful to two anonymous referees whose excellent comments have improved the paper substantially. I acknowledge NASA funding through the awards 80NSSC18K0264 and NNX16AC42G.


  1. 1.
    Abbott, B.P., et al.: (LIGO Scientific Collaboration), Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016)Google Scholar
  2. 2.
    Abbott, B.P., et al.: (LIGO Scientific Collaboration), Tests of general relativity with GW150914. Phys. Rev. Lett. 116, 1101 (2016)Google Scholar
  3. 3.
    Abbott, B.P., et al.: (LIGO Scientific Collaboration), GW151226: Observation of gravitational waves from a 22-solar-mass binary black hole coalescence. Phys. Rev. Lett. 116, 241103 (2016)Google Scholar
  4. 4.
    Abbott, B.P., et al.: (LIGO Scientific Collaboration), GW170104: Observation of a 50-solar-mass binary black hole coalescence at redshift 0.2. Phys. Rev. Lett. 118, 221101 (2017)Google Scholar
  5. 5.
    Abbott, B.P., et al.: (LIGO Scientific Collaboration), GW170608: Observation of a 19-solar-mass binary black hole coalescence. Astrophys J Lett. 851(2), L35 (2017)Google Scholar
  6. 6.
    Abbott, B.P., et al.: (LIGO Scientific Collaboration), GW170814: a three-detector observation of gravitational waves from a binary black hole coalescence. Phys. Rev. Lett. 119, 141101 (2017)Google Scholar
  7. 7.
    Abbott, B.P., et al.: (LIGO Scientific Collaboration), GW170817: observation of gravitational waves from a binary neutron star inspiral. Phys. Rev. Lett. 119, 161101 (2017)Google Scholar
  8. 8.
    Abramowicz, M.A.: QPO as the Rosetta Stone for understanding black hole accretion. Astron. Nachr. 326, 782A (2005)ADSzbMATHGoogle Scholar
  9. 9.
    Abramowicz, M.A., Fragile, P.C.: Foundations of black hole accretion disk theory. Living Rev. Relativ. 16, 1 (2013). ADSGoogle Scholar
  10. 10.
    Abramowicz, M.A., Kluźniak, W.: A precise determination of black hole spin in GRO J1655–40. Astron. Astrophys. 374L, 19A (2001)Google Scholar
  11. 11.
    Akiyama, K., Kuramochi, K., Ikeda, S., et al.: Imaging the Schwarzschild-radius-scale structure of M87 with the event horizon telescope using sparse modeling. Astrophys. J. 838, 1 (2017).
  12. 12.
    Aliev, A.N., Gümrükçüoǧlu, A.E.: Charged rotating black holes on a 3-brane. Phys. Rev. D 71, 104027 (2005)ADSMathSciNetGoogle Scholar
  13. 13.
    Ayzenberg, D., Yunes, N.: Black hole continuum spectra as a test of general relativity: quadratic gravity. Class. Quantum Gravity 34, 115003 (2017)ADSMathSciNetzbMATHGoogle Scholar
  14. 14.
    Balbus, S.A., Hawley, J.F.: Instability, turbulence, and enhanced transport in accretion disks. Rev. Mod. Phys. 70, 1 (1998)ADSGoogle Scholar
  15. 15.
    Bambi, C.: A code to compute the emission of thin accretion disks in non-Kerr spacetimes and test the nature of black hole candidates. Astrophys. J. 761, 174B (2012)ADSGoogle Scholar
  16. 16.
    Bambi, C.: Testing the space-time geometry around black hole candidates with the analysis of the broad \(\text{ K }\alpha \) iron line. Phys. Rev. D 87, 023007 (2013)ADSGoogle Scholar
  17. 17.
    Bambi, C., Cárdenas-Avendaño, A., Dauser, T., García, J.A.: Testing the Kerr black hole hypothesis using X-ray reflection spectroscopy. Astrophys. J. 842, 76B (2017)ADSGoogle Scholar
  18. 18.
    Bambi, C., Jiang, J., Steiner, J.F.: Testing the no-hair theorem with the continuum-fitting and the iron line methods: a short review. Class. Quantum Gravity 33, 064001 (2016)ADSGoogle Scholar
  19. 19.
    Bardeen, J.M., Petterson, J.A.: The Lense–Thirring effect and accretion disks around Kerr black holes. Astrophys. J. 195, L65–L67 (1975)ADSGoogle Scholar
  20. 20.
    Baumgarte, T.W., Shapiro, S.L.: Numerical Relativity: Solving Einstein’s Equations on the Computer Publisher, 1st edn. Cambridge University Press, Cambridge (2010)zbMATHGoogle Scholar
  21. 21.
    Beheshtipour, B., Krawczynski, H., Malzac, J.: The X-ray polarization of the accretion disk coronae of active galactic nuclei. Astrophys. J. 850, 14B (2017)ADSGoogle Scholar
  22. 22.
    Berti, E., et al.: Testing general relativity with present and future astrophysical observations. Class. Quantum Gravity 32, 243001 (2015)ADSGoogle Scholar
  23. 23.
    Blackburne, J.A., Kochanek, C.S., Chen, B., Dai, X., Chartas, G.: The structure of HE 1104–1805 from infrared to X-ray. Astrophys. J. 798, 95B (2015)ADSGoogle Scholar
  24. 24.
    Blandford, R.D., Znajek, R.L.: Electromagnetic extraction of energy from Kerr black holes. Mon. Not. R. Astron. Soc. 179, 433 (1977)ADSGoogle Scholar
  25. 25.
    Boller, T., Müller, A.: Observational tests of the pseudo-complex theory of GR using black hole candidates. In: Greiner, W. (ed.) Nuclear Physics: Present and Future. FIAS Interdisciplinary Science Series, pp. 245–253. Springer, Cham (2015)Google Scholar
  26. 26.
    Boyer, R.H., Lindquist, R.W.: Maximal analytic extension of the Kerr metric. J. Math. Phys. 8, 265 (1967)ADSMathSciNetzbMATHGoogle Scholar
  27. 27.
    Brenneman, L.: Measuring supermassive black hole spins in AGN. Acta Polytech. Suppl. 53, 652 (2013)ADSGoogle Scholar
  28. 28.
    Brenneman, L.W., Reynolds, C.S.: Constraining black hole spin via X-ray spectroscopy. Astrophys. J. 652, 1028B (2006)ADSGoogle Scholar
  29. 29.
    Cardoso, V., Pani, P., Rico, J.: On generic parametrizations of spinning black-hole geometries. Phys. Rev. D. 89, 064007 (2014)ADSGoogle Scholar
  30. 30.
    Carroll, S.: Spacetime and Geometry: An Introduction To General Relativity. Pearson, first edition, Appendix B (2003)Google Scholar
  31. 31.
    Carter, B.: Global structure of the Kerr family of gravitational fields. Phys. Rev. 174, 1559 (1968)ADSzbMATHGoogle Scholar
  32. 32.
    Carter, B.: Hamilton–Jacobi and Schrodinger separable solutions of Einstein’s equations. Commun. Math. Phys. 10, 280 (1968)ADSMathSciNetzbMATHGoogle Scholar
  33. 33.
    Carter, B.: Axisymmetric black hole has only two degrees of freedom. Phys. Rev. Lett. 26, 331 (1971)ADSGoogle Scholar
  34. 34.
    Carter, B.: Black hole equilibrium states. In: DeWitt, C., DeWitt, B.S. (eds.) Les Houches 1972, Black Holes, Les Astres Occlus, 1st edn. Gordon and Breach, New York (1973)Google Scholar
  35. 35.
    Castor, J.I.: Radiation Hydrodynamics. Cambridge University Press, Cambridge (2004)Google Scholar
  36. 36.
    Chandrasekhar, S.: The Mathematical Theory of Black Holes. Oxford University Press, New York (1983, Reprint 2010)Google Scholar
  37. 37.
    Chartas, G., Agol, E., Eracleous, M., Garmire, G., Bautz, M.W., Morgan, N.D.: Caught in the act: Chandra observations of microlensing of the radio-loud Quasar MG J0414+ 0534. Astrophys. J. 568, 509C (2002)ADSGoogle Scholar
  38. 38.
    Chartas, G., Kochanek, C.S., Dai, X., Moore, D., Mosquera, A.M., Blackburne, J.A.: Revealing the structure of an accretion disk through energy-dependent X-ray microlensing. Astrophys. J. 757, 137C (2012)ADSGoogle Scholar
  39. 39.
    Chartas, G., Kochanek, C.S., Dai, X., Poindexter, S., Garmire, G.: X-ray microlensing in RXJ1131-1231 and HE1104-1805. Astrophys. J. 693, 174 (2009)ADSGoogle Scholar
  40. 40.
    Chartas, G., Krawczynski, H., Zalesky, L., Kochanek, C.S., Dai, X., Morgan, C.W., Mosquera, A.: Measuring the innermost stable circular orbits of supermassive black holes. Astrophys. J. 837, 26C (2017)ADSGoogle Scholar
  41. 41.
    Chiang, C.-Y., Walton, D.J., Fabian, A.C., Wilkins, D.R., Gallo, L.C.: Modelling the extreme X-ray spectrum of IRAS 13224–3809. Mon. Not. R. Astron. Soc. 446, 759 (2015)ADSGoogle Scholar
  42. 42.
    Dai, X., Kochanek, C.S., Chartas, G., Kozłowski, S., Morgan, C.W., Garmire, G., Agol, E.: The sizes of the X-ray and optical emission regions of RXJ 1131–1231. Astrophys. J. 709, 278D (2010)ADSGoogle Scholar
  43. 43.
    Dauser, T., Garcia, J., Wilms, J.: Irradiation of an accretion disc by a jet: general properties and implications for spin measurements of black holes. Mon. Not. R. Astron. Soc. 430, 1694–1708 (2013)ADSGoogle Scholar
  44. 44.
    Davis, S.W., Blaes, O.M., Hubeny, I., Turner, N.J.: Relativistic accretion disk models of high-state black hole X-ray binary spectra. Astrophys. J. 621, 372D (2005)ADSGoogle Scholar
  45. 45.
    Davis, S.W., Done, C., Blaes, O.M.: Testing accretion disk theory in black hole X-ray binaries. Astrophys. J. 647, 525 (2006)ADSGoogle Scholar
  46. 46.
    Demianski, M., Ivanov, P.B.: The dynamics of twisted accretion disc around a Kerr black hole. Astron. Astrophys. 324, 829D (1997)ADSGoogle Scholar
  47. 47.
    Dovčiak, M., Karas, V., Matt, G., et al.: Polarization signatures of strong gravity in active galactic nuclei accretion discs. Mon. Not. R. Astron. Soc. 355, 1005D (2004)ADSGoogle Scholar
  48. 48.
    Dovčiak, M., Done, C.: Minimum X-ray source size of the on-axis corona in AGN. Astron. Nachr. 337, 441 (2016)ADSGoogle Scholar
  49. 49.
    Duro, R., Dauser, T., Wilms, J.: The broad iron \(\text{ K }\alpha \) line of Cygnus X-1 as seen by XMM-Newton in the EPIC-pn modified timing mode. Astron. Astrophys. 533, L3 (2011)ADSGoogle Scholar
  50. 50.
    Edelson, R., Gelbord, J.M., Horne, K., et al.: Space telescope and optical reverberation mapping project. II. Swift and HST reverberation mapping of the accretion disk of NGC 5548. Astrophys. J. 806, 129 (2015)ADSGoogle Scholar
  51. 51.
    Elvis, M., Wilkes, B.J., McDowell, J.C., et al.: Atlas of quasar energy distributions. Astrophys. J. Suppl. 95, 1 (1994)ADSGoogle Scholar
  52. 52.
    Fabian, A.C.: The innermost extremes of black hole accretion. Astron. Nachr. 337, 375F (2016)ADSGoogle Scholar
  53. 53.
    Fabian, A.C., Rees, M.J., Stella, L., White, N.E.: X-ray fluorescence from the inner disc in Cygnus X-1. Mon. Not. R. Astron. Soc. 238, 729F (1989)ADSGoogle Scholar
  54. 54.
    Fabian, A.C., Zoghbi, A., Ross, R.R., et al.: Broad line emission from iron K- and L-shell transitions in the active galaxy 1H0707-495. Nature 459, 540 (2009)ADSGoogle Scholar
  55. 55.
    Fabian, A.C., Wilkins, D.R., Miller, J.M.: On the determination of the spin of the black hole in Cyg X-1 from X-ray reflection spectra. Mon. Not. R. Astron. Soc. 424, 217 (2012)ADSGoogle Scholar
  56. 56.
    Fender, R.P., Garrington, S.T., McKay, D.J., et al.: MERLIN observations of relativistic ejections from GRS 1915+ 105. Mon. Not. R. Astron. Soc. 304, 865F (1999)ADSGoogle Scholar
  57. 57.
    Feng, Y., Ramesh, N.: Hot accretion flows around black holes. Annu. Rev. Astron. Astrophys. 52, 529 (2014)Google Scholar
  58. 58.
    Fock, V.: The Theory of Space, Time and Gravitation. Pergamon Press, New York (1964)zbMATHGoogle Scholar
  59. 59.
    Fodor, G.: Multipole moments of axisymmetric systems in relativity. J. Math. Phys. 30, 2252 (1989)ADSMathSciNetzbMATHGoogle Scholar
  60. 60.
    Foucart, F., Chandra, M., Gammie, C.F., Quataert, E., Tchekhovskoy, A.: How important is non-ideal physics in simulations of sub-Eddington accretion on to spinning black holes? Mon. Not. R. Astron. Soc. 470, 2240F (2017)ADSGoogle Scholar
  61. 61.
    Fragile, P.C., Blaes, O.M., Anninos, P., Salmonson, J.D.: Global general relativistic magnetohydrodynamic simulation of a tilted black hole accretion disk. Astrophys. J. 668, 417–429 (2007)ADSGoogle Scholar
  62. 62.
    Fragile, P.C., Lindner, C.C., Anninos, P., Salmonson, J.D.: Application of the cubed-sphere grid to tilted black hole accretion disks. Astrophys. J. 691, 482F (2009)ADSGoogle Scholar
  63. 63.
    Fürst, F., Nowak, M.A., Tomsick, J.A., et al.: The complex accretion geometry of GX 339–4 as seen by NuSTAR and SWIFT. Astrophys. J. 808, 122 (2015)ADSGoogle Scholar
  64. 64.
    Gair, J.A., Vallisneri, M., Larson, S.L., Baker, J.G.: Testing general relativity with low-frequency, space-based gravitational-wave detectors. Living Rev. Relativ. 16, 7 (2013).
  65. 65.
    García, J.A., Dauser, T., Lohfink, A.: Improved reflection models of black hole accretion disks: treating the angular distribution of X-rays. Astrophys. J. 782, 76G (2014)ADSGoogle Scholar
  66. 66.
    García, J.A., Dauser, T., Reynolds, C.S., Kallman, T.R., McClintock, J.E., Wilms, J., Eikmann, W.: X-ray reflected spectra from accretion disk models. III. A complete grid of ionized reflection calculations. Astrophys. J. 768, 146 (2013)ADSGoogle Scholar
  67. 67.
    García, J.A., Fabian, A.C., Kallman, T.R., Dauser, T., Parker, M.L., McClintock, J.E., Steiner, J.F., Wilms, J.: The effects of high density on the X-ray spectrum reflected from accretion discs around black holes. Mon. Not. R. Astron. Soc. 462, 751–760 (2016)ADSGoogle Scholar
  68. 68.
    García, J.A., Steiner, J.F., McClintock, J.E., Remillard, R.A.: X-ray reflection spectroscopy of the black hoLE GX 339–4: exploring the hard state with unprecedented sensitivity. Astrophys. J. 813, 84 (2015)ADSGoogle Scholar
  69. 69.
    Geroch, R.: Multipole moments. II. Curved space. J. Math. Phys. (N.Y.) 11, 2580 (1970)ADSMathSciNetzbMATHGoogle Scholar
  70. 70.
    Ghasemi-Nodehi, M., Bambi, C.: Constraining the Kerr parameters via X-ray reflection spectroscopy. Phys. Rev. D 94, 104062 (2016)ADSGoogle Scholar
  71. 71.
    Gierliński, M., Maciołek-Niedźwiecki, A., Ebisawa, K.: Application of a relativistic accretion disc model to X-ray spectra of LMC X-1 and GRO J1655–40. Mon. Not. R. Astron. Soc. 325, 1253G (2001)ADSGoogle Scholar
  72. 72.
    Gilfanov, M., Merloni, A.: Observational appearance of black holes in X-ray binaries and AGN. Space Sci. Rev. 183, 121 (2014)ADSGoogle Scholar
  73. 73.
    Glampedakis, K., Babak, S.: Mapping spacetimes with LISA: inspiral of a test body in a ’quasi-Kerr’ field. Class. Quantum Gravity 23, 4167–4188 (2006)ADSMathSciNetzbMATHGoogle Scholar
  74. 74.
    Gonzalez, A.G., Wilkins, D.R., Gallo, L.C.: Probing the geometry and motion of AGN coronae through accretion disc emissivity profiles. Mon. Not. R. Astron. Soc. 472, 1932G (2017)ADSGoogle Scholar
  75. 75.
    Gou, L., McClintock, J.E., Liu, J.: A determination of the spin of the black hole primary in LMC X-1. Astrophys. J. 701, 1076–1090 (2009)ADSGoogle Scholar
  76. 76.
    Gou, L., McClintock, J.E., Reid, M.J., et al.: The extreme spin of the black hole in Cygnus X-1. Astrophys. J. 742, 85G (2011)ADSGoogle Scholar
  77. 77.
    Gou, L., McClintock, J.E., Remillard, R.A.: Confirmation via the continuum-fitting method that the spin of the black hole in Cygnus X-1 is extreme. Astrophys. J. 790, 29 (2014)ADSGoogle Scholar
  78. 78.
    Greene, J., Bailyn, C.D., Orosz, J.A.: Optical and infrared photometry of the microquasar GRO J1655–40 in quiescence. Astrophys. J. 554, 1290G (2001)ADSGoogle Scholar
  79. 79.
    Hall, P., Sarrouh, G., Horne, K.: Non-blackbody disks can help explain inferred AGN accretion disk sizes, submitted to Astrophys. J. (2017). arXiv:1705.05467
  80. 80.
    Hansen, R.O.: Multipole moments of stationary space-times. J. Math. Phys. (N.Y.) 15, 46 (1974)ADSMathSciNetzbMATHGoogle Scholar
  81. 81.
    Hawking, S.W.: Gravitational radiation from colliding black holes. Phys. Rev. Lett. 26, 1344–1346 (1971)ADSGoogle Scholar
  82. 82.
    Hawking, S.W.: Black holes in general relativity. Commun. Math. Phys. 25, 152–166 (1972)ADSMathSciNetGoogle Scholar
  83. 83.
    Heusler, M.: Black Hole Uniqueness Theorems. Cambridge University Press, Cambridge (1996)zbMATHGoogle Scholar
  84. 84.
    Chruściel, P.T., Costa, J.L., Heusler, M.: Stationary black holes: uniqueness and beyond. Living Rev. Relativ. 15, 7 (2012).
  85. 85.
    Hoormann, J.K., Beheshtipour, B., Krawczynski, H.: Testing general relativity’s no-hair theorem with X-ray observations of black holes. Phys. Rev. D. 93, 044020 (2016)ADSGoogle Scholar
  86. 86.
    Ingram, A., Done, C., Fragile, P.C.: Low-frequency quasi-periodic oscillations spectra and Lense–Thirring precession. Mon. Not. R. Astron. Soc. 397, L101–L105 (2009)ADSGoogle Scholar
  87. 87.
    Ingram, A., Maccarone, T.J., Poutanen, J., Krawczynski, H.: Polarization modulation from lense-thirring precession in X-ray binaries. Astrophys. J. 807, 53I (2015)ADSGoogle Scholar
  88. 88.
    Ingram, A., Maccarone, T.J.: An observational method for fast stochastic X-ray polarimetry timing. Mon. Not. R. Astron. Soc. 471, 4206–4217 (2017)ADSGoogle Scholar
  89. 89.
    Israel, W.: Event horizons in static vacuum space-times. Phys. Rev. 164, 1776 (1967)ADSGoogle Scholar
  90. 90.
    Israel, W.: Event horizons in static electrovac space-times. Commun. Math. Phys. 8, 245 (1968)ADSMathSciNetGoogle Scholar
  91. 91.
    Ivanov, P.B., Illarionov, A.F.: The oscillatory shape of the stationary twisted disc around a Kerr black hole. Mon. Not. R. Astron. Soc. 285, 394–402 (1997)ADSGoogle Scholar
  92. 92.
    Jiang, Y.F., Davis, S.W., Stone, J.M.: Iron opacity bump changes the stability and structure of accretion disks in active galactic nuclei. Astrophys. J. 827, 10 (2016)ADSGoogle Scholar
  93. 93.
    Jiang, Y.-F., et al.: Detection of time lags between quasar continuum emission bands based on Pan-STARRS light curves. Astrophys. J. 836, 186 (2017)ADSGoogle Scholar
  94. 94.
    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)ADSGoogle Scholar
  95. 95.
    Johannsen, T.: Regular black hole metric with three constants of motion. Phys. Rev. D. 88, 044002 (2013)ADSGoogle Scholar
  96. 96.
    Johannsen, T., Psaltis, D.: Testing the no-hair theorem with observations in the electromagnetic spectrum. IV. Relativistically broadened iron lines. Astrophys. J. 773, 57J (2013)ADSGoogle Scholar
  97. 97.
    Johannsen, T.: Systematic study of event horizons and pathologies of parametrically deformed Kerr spacetimes. Phys. Rev. D. 87, 124017 (2013)ADSGoogle Scholar
  98. 98.
    Johannsen, T.: Photon rings around Kerr and Kerr-like black holes. Astrophys. J. 777, 117 (2013)Google Scholar
  99. 99.
    Johannsen, T.: X-ray probes of black hole accretion disks for testing the no-hair theorem. Phys. Rev. D 90, 064002 (2014)ADSGoogle Scholar
  100. 100.
    Johannsen, T.: Testing the no-hair theorem with observations of black holes in the electromagnetic spectrum. Class. Quantum Gravity 33, 124001 (2016)ADSGoogle Scholar
  101. 101.
    Kerr, R.P.: Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11, 237 (1963)ADSMathSciNetzbMATHGoogle Scholar
  102. 102.
    Khargharia, J., Froning, C.S., Robinson, E.L.: near-infrared spectroscopy of low-mass X-ray binaries: accretion disk contamination and compact object mass determination in V404 CYG and Cen X-4. Astrophys. J. 716, 1105–1117 (2010)ADSGoogle Scholar
  103. 103.
    Kislat, F., Beheshtipour, B., Dowkontt, P., et al.: Design of the telescope Truss and Gondola for the balloon-borne X-ray polarimeter X-Calibur. J. Astron. Instrum. 6, 1740003 (2017)Google Scholar
  104. 104.
    Kleihaus, B., Kunz, J., Radu, E.: Rotating black holes in dilatonic Einstein–Gauss–Bonnet theory. Phys. Rev. Lett. 106, 151104 (2011)ADSGoogle Scholar
  105. 105.
    Kolehmainen, M., Done, C.: Limits on spin determination from disc spectral fitting in GX \(339-4\). Mon. Not. R. Astron. Soc. 406, 2206–2212 (2010)ADSGoogle Scholar
  106. 106.
    Kolehmainen, M., Done, C., Díaz Trigo, M.: Modelling the high-mass accretion rate spectra of GX 339–4: black hole spin from reflection? Mon. Not. R. Astron. Soc. 416, 311–321 (2011)ADSGoogle Scholar
  107. 107.
    Kong, L., Li, Z., Bambi, C.: Constraints on the spacetime geometry around 10 stellar-mass black hole candidates from the disk’s thermal spectrum. Astrophys. J. 797, 78 (2014)ADSGoogle Scholar
  108. 108.
    Konoplya, R., Rezzolla, L., Zhidenko, A.: General parametrization of axisymmetric black holes in metric theories of gravity. Phys. Rev. D. 93, 064015 (2016)ADSMathSciNetGoogle Scholar
  109. 109.
    Krawczynski, H.: Tests of general relativity in the strong-gravity regime based on X-ray spectropolarimetric observations of black holes in X-ray binaries. Astrophys. J. 754, 133 (2012)ADSGoogle Scholar
  110. 110.
    Krawczynski, H., Chartas, G.: Modeling of the microlensed \(\text{ Fe } \text{ K }\alpha \) emission from the Quasar RX J1131–1231. Astrophys. J. Lett. 843, 118K (2017)ADSGoogle Scholar
  111. 111.
    Krawczynski, H., Stern, D., Harrison, F.A., et al.: X-ray polarimetry with the Polarization Spectroscopic Telescope Array (PolSTAR). Astropart. Phys. 75, 8K (2016)ADSGoogle Scholar
  112. 112.
    Kulkarni, A.K., Penna, R.F., Shcherbakov, R.V., et al.: Measuring black hole spin by the continuum-fitting method: effect of deviations from the Novikov–Thorne disc model. Mon. Not. R. Astron. Soc. 414, 1183 (2011)ADSGoogle Scholar
  113. 113.
    Kumar, S., Pringle, J.E.: Twisted accretion disks: the Bardeen–Petterson effect. Mon. Not. R. Astron. Soc. 213, 435–442 (1985)ADSGoogle Scholar
  114. 114.
    Lense, J., Thirring, H.: Über die Einfluß der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Zeit. Phys. 19, 156–163 (1918)zbMATHGoogle Scholar
  115. 115.
    Li, L.-X., Narayan, R., McClintock, J.E., et al.: Inferring the inclination of a black hole accretion disk from observations of its polarized continuum radiation. Astrophys. J. Lett. 691, 847L (2009)Google Scholar
  116. 116.
    LIGOScientific Collaboration and Virgo Collaboration: Fermi Gamma-ray Burst Monitor, and INTEGRAL, Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A. Astrophys. J. Lett. 848, L13 (2017)Google Scholar
  117. 117.
    Lubow, S.H., Ogilvie, G.I., Pringle, J.E.: The evolution of a warped disc around a Kerr black hole. Mon. Not. R. Astron. Soc. 337, 706–712 (2002)ADSGoogle Scholar
  118. 118.
    Maccarone, T.J.: On the misalignment of jets in microquasars. Mon. Not. R. Astron. Soc. 336, 1371 (2002), Erratum: On the misalignment of jets in microquasars. Mon. Not. R. Astron. Soc. 446, 3162M (2015)Google Scholar
  119. 119.
    MacLeod, C.L., Morgan, C.W., Mosquera, A., et al.: A consistent picture emerges: a compact X-ray continuum emission region in the gravitationally lensed quasar SDSS J0924+0219. Astrophys. J. 806, 258M (2015)ADSGoogle Scholar
  120. 120.
    Marin, F., Dovčiak, M., Muleri, F., Kislat, F.F., Krawczynski, H.S.: Predicting the X-ray polarization of type 2 Seyfert galaxies. Mon. Not. R. Astron. Soc. 473, 1286M (2018)ADSGoogle Scholar
  121. 121.
    Marshall, M.D., Avara, M.J., McKinney, J.C.: Angular momentum transport in thin magnetically arrested disks (2017). arXiv:1709.10113
  122. 122.
    Martin, R.G., Tout, C.A., Pringle, J.E.: Alignment time-scale of the microquasar GRO J1655–40. Mon. Not. R. Astron. Soc. 387, 188 (2008)ADSGoogle Scholar
  123. 123.
    Matt, G., Perola, G.C., Piro, L.: The iron line and high energy bump as X-ray signatures of cold matter in Seyfert 1 galaxies. Astron. Astrophys. 247, 25 (1991)ADSGoogle Scholar
  124. 124.
    Mazur, P.O.: Proof of uniqueness of the Kerr–Newman black hole solution. J. Phys. A Math. Gen. 15, 3173–3180 (1982)ADSMathSciNetzbMATHGoogle Scholar
  125. 125.
    Mazur, P.O.: Black Hole Uniqueness Theorems. (2009)
  126. 126.
    McClintock, J.E., Narayan, R., Steiner, J.F.: Black hole spin via continuum fitting and the role of spin in powering transient jets. Space Sci. Rev. 183, 295M (2014)ADSGoogle Scholar
  127. 127.
    McClintock, J.E., Shafee, R., Narayan, R., Remillard, R.A., Davis, S.W., Li, L.-X.: The spin of the near-extreme Kerr black hole GRS 1915+105. Astrophys. J. 652, 518–539 (2006)ADSGoogle Scholar
  128. 128.
    Middleton, M., Done, C., Gierliński, M., Davis, S.W.: Black hole spin in GRS 1915+105. Mon. Not. R. Astron. Soc. 373, 1004–1012 (2006)ADSGoogle Scholar
  129. 129.
    Miller, J.M.: Relativistic X-ray lines from the inner accretion disks around black holes. Ann. Rev. Astron. Astrophys. 45, 441–79 (2007)ADSGoogle Scholar
  130. 130.
    Miller, J.M., Pooley, G.G., Fabian, A.C., et al.: On the role of the accretion disk in black hole disk-jet connections. Astrophys. J. 757, 11 (2012)ADSGoogle Scholar
  131. 131.
    Miller, J.M., Parker, M.L., Fürst, F., et al.: NuSTAR spectroscopy OF GRS 1915+105: disk reflection, spin, and connections to jets. Astrophys. J. Lett. 775, L45 (2013)ADSGoogle Scholar
  132. 132.
    Miller, J.M., Reynolds, C.S., Fabian, A.C., Miniutti, G., Gallo, L.C.: Stellar-mass black hole spin constraints from disk reflection and continuum modeling. Astrophys. J. 697, 900M (2009)ADSGoogle Scholar
  133. 133.
    Mishra, B., Fragile, P.C., Johnson, L.C., Kluźniak, W.: Three-dimensional, global, radiative GRMHD simulations of a thermally unstable disc. Mon. Not. R. Astron. Soc. 463, 3437M (2016)ADSGoogle Scholar
  134. 134.
    Morales Teixeira, D., Fragile, P.C., Zhuravlev, V.V., Ivanov, P.B.: Conservative grmhd simulations of moderately thin, tilted accretion disks. Astrophys. J. 796, 103 (2014)ADSGoogle Scholar
  135. 135.
    Morgan, C.W., Kochanek, C.S., Morgan, N.D., Falco, E.E.: The quasar accretion disk size-black hole mass relation. Astrophys. J. 712, 1129 (2010)ADSGoogle Scholar
  136. 136.
    Morgan, C.W., et al.: Further evidence that quasar X-ray emitting regions are compact: X-ray and optical microlensing in the lensed quasar Q J0158–4325. Astrophys. J. 756, 52 (2012)ADSGoogle Scholar
  137. 137.
    Mosquera, A.M.: The structure of the X-ray and optical emitting regions of the lensed quasar Q 2237+0305. Astrophys. J. 769, 53 (2013)ADSGoogle Scholar
  138. 138.
    Nandra, K.: ATHENA: the advanced telescope for high energy astrophysics, The X-ray Universe 2011, Berlin, Germany, 27-30 June 2011 (2011).
  139. 139.
    Narayan, R., Zhu, Y., Psaltis, D., Sa̧dowski, A.: HEROIC: 3D general relativistic radiative post-processor with comptonization for black hole accretion discs. Mon. Not. R. Astron. Soc. 457, 608 (2016)ADSGoogle Scholar
  140. 140.
    Neustroev, V.V., Veledina, A., Poutanen, J., Zharikov, S.V., Tsygankov, S.S., Sjoberg, G., Kajava, J.J.E.: Spectroscopic evidence for a low-mass black hole in SWIFT J1753.5-0127. Mon. Not. R. Astron. Soc. 445, 2424N (2014)ADSGoogle Scholar
  141. 141.
    Newman, E., Adamo, T.: Kerr-Newman metric. Scholarpedia 9, 31791 (2014).
  142. 142.
    Newman, E.T., Couch, E., Chinnapared, K., Exton, A., Prakash, A., Torrence, R.: Metric of a rotating, Charged mass. J. Math. Phys. 6, 918 (1965)ADSMathSciNetGoogle Scholar
  143. 143.
    Noble, S.C., et al.: Radiative efficiency and thermal spectrum of accretion onto Schwarzschild black holes. Astrophys. J. 743, 115 (2011)ADSGoogle Scholar
  144. 144.
    Novikov, I.D., Thorne, K.S.: Black hole equilibrium states. In: DeWitt, C., DeWitt, B.S. (eds.) Les Houches 1972, Black Holes, Les Astres Occlus, 1st edn, pp. 343–450. Gordon and Breach, New York (1973)Google Scholar
  145. 145.
    Orosz, J.A., McClintock, J.E., Remillard, R.A., Corbel, S.: Orbital parameters for the black hole binary XTE J1650–500. Astrophys. J. 616, 376O (2004)ADSGoogle Scholar
  146. 146.
    Orosz, J.A., McClintock, J.E., Aufdenberg, J.P., Remillard, R.A., Reid, M.J., Narayan, R., Gou, L.: The mass of the black hole in Cygnus X-1. Astrophys. J. 742, 84O (2011)ADSGoogle Scholar
  147. 147.
    Page, D.N., Thorne, K.S.: Disk-accretion onto a black hole. Time-averaged structure of accretion disk. Astrophys. J. 191, 499 (1974)ADSGoogle Scholar
  148. 148.
    Pani, P., Macedo, C.F.B., Crispino, L.C.B., Cardoso, V.: Slowly rotating black holes in alternative theories of gravity. Phys. Rev. D 84, 087501 (2011)ADSGoogle Scholar
  149. 149.
    Papaloizou, J.C.B., Lin, D.N.C.: On the dynamics of warped accretion disks. Astrophys. J. 438, 841P (1995)ADSGoogle Scholar
  150. 150.
    Papaloizou, J.C.B., Pringle, J.E.: The time-dependence of non-planar accretion disks. Mon. Not. R. Astron. Soc. 202, 1181–1194 (1983)ADSzbMATHGoogle Scholar
  151. 151.
    Parker, M.L., Tomsick, J.A., Kennea, J.A., et al.: NuSTAR and SWIFT observations of the very high state in GX 339-4: weighing the black hole with X-rays. Astrophys. J. Lett. 821, L6 (2016)ADSGoogle Scholar
  152. 152.
    Penna, R.F., Sa̧dowski, A., McKinney, J.C.: Thin-disc theory with a non-zero-torque boundary condition and comparisons with simulations. Mon. Not. R. Astron. Soc. 420, 684–698 (2012)ADSGoogle Scholar
  153. 153.
    Poisson, E., Will, C.M.: Gravity: Newtonian, Post-Newtonian, Relativistic, 1st edn. Cambridge University Press, Cambridge (2014)zbMATHGoogle Scholar
  154. 154.
    Psaltis, D.: Probes and tests of strong-field gravity with observations in the electromagnetic spectrum. Living Rev. Relativ. 11, 9 (2008). 10.12942/lrr-2008-9ADSzbMATHGoogle Scholar
  155. 155.
    Psaltis, D., Johannsen, T.: A ray-tracing algorithm for spinning compact object spacetimes with arbitrary quadrupole moments. I. Quasi-Kerr black holes. Astrophys. J. 745, 6 (2012)ADSGoogle Scholar
  156. 156.
    Remillard, R.A., McClintock, J.E.: X-ray properties of black-hole binaries. Ann. Rev. Astron. Astrophys. 44, 49R (2006)ADSGoogle Scholar
  157. 157.
    Reid, M.J., McClintock, J.E., Narayan, R., Gou, L., Remillard, R.A., Orosz, J.A.: The trigonometric parallax of Cygnus X-1. Astrophys. J. 742, 83R (2011)ADSGoogle Scholar
  158. 158.
    Reid, M.J., McClintock, J.E., Steiner, J.F., Steeghs, D., Remillard, R.A., Dhawan, V., Narayan, R.: A parallax distance to the microquasar GRS 1915+ 105 and a revised estimate of its black hole mass. Astrophys. J. 796, 2 (2014)ADSGoogle Scholar
  159. 159.
    Reis, R.C., Fabian, A.C., Ross, R.R., Miller, J.M.: Determining the spin of two stellar-mass black holes from disc reflection signatures. Mon. Not. R. Astron. Soc. 395, 1257–1264 (2009)ADSGoogle Scholar
  160. 160.
    Reis, R.C., Fabian, A.C., Ross, R.R., Miniutti, G., Miller, J.M., Reynolds, C.: A systematic look at the very high and low/hard state of GX \(339-4\): constraining the black hole spin with a new reflection model. Mon. Not. R. Astron. Soc. 387, 1489–1498 (2008)ADSGoogle Scholar
  161. 161.
    Reis, R.C., Miller, J.M., Reynolds, M.T., Fabian, A.C., Walton, D.J.: Suzaku observation of the black hole candidate maxi J1836–194 in a hard/intermediate spectral state. Astrophys. J. 751, 34R (2012)ADSGoogle Scholar
  162. 162.
    Reis, R.C., Reynolds, M.T., Miller, J.M., Walton, D.J.: Reflection from the strong gravity regime in a z = 0.658 gravitationally lensed-quasar. Nature 507, 207 (2014)ADSGoogle Scholar
  163. 163.
    Reynolds, C.S., Fabian, A.C.: Special relativistic effects on the strength of the fluorescent Kalpha iron line from black hole accretion discs. Mon. Not. R. Astron. Soc. 290L, 1R (1997)ADSGoogle Scholar
  164. 164.
    Risaliti, G., Harrison, F.A., Madsen, K.K., et al.: A rapidly spinning supermassive black hole at the centre of NGC 1365. Nature 494, 449–451 (2013)ADSGoogle Scholar
  165. 165.
    Robinson, D.C.: Uniqueness of the Kerr black hole. Phys. Rev. Lett. 34, 905–906 (1975)ADSGoogle Scholar
  166. 166.
    Robinson, D.C.: Four decades of black hole uniqueness theorems. In: Wiltshire, D.L., Visser, M., Scott, S.M. (eds.) The Kerr Spacetime: Rotating Black Holes in General Relativity, pp. 115–143. Cambridge University Press, Cambridge (2009).
  167. 167.
    Ross, R.R., Fabian, A.C.: A comprehensive range of X-ray ionized-reflection models. Mon. Not. R. Astron. Soc. 358, 211 (2005)ADSGoogle Scholar
  168. 168.
    Russell, T.D., Soria, R., Motch, C.: The face-on disc of MAXI J1836–194. Mon. Not. R. Astron. Soc. 439, 1381–1389 (2014)ADSGoogle Scholar
  169. 169.
    Ryan, F.D.: Gravitational waves from the inspiral of a compact object into a massive, axisymmetric body with arbitrary multipole moments. Phs. Rev. D 52, 5707R (1995)ADSGoogle Scholar
  170. 170.
    Ryan, B.R., Ressler, S.M., Dolence, J.C., Tchekhovskoy, A., Gammie, C., Quataert, E.: The radiative efficiency and spectra of slowly accreting black holes from two-temperature GRRMHD simulations. Astrophys. J. Lett. 844L, 24R (2017)ADSGoogle Scholar
  171. 171.
    Sa̧dowski, A., Narayan, R.: Three-dimensional simulations of supercritical black hole accretion discs—luminosities, photon trapping and variability. Mon. Not. R. Astron. Soc. 456, 3929 (2016)ADSGoogle Scholar
  172. 172.
    Schnittman, J.D., Homan, J., Miller, J.M.: A precessing ring model for low-frequency quasi-periodic oscillations. Astrophys. J. 642, 420S (2006)ADSGoogle Scholar
  173. 173.
    Schnittman, J.D., Krolik, J.H.: X-ray polarization from accreting black holes: the thermal state. Astrophys. J. 701, 1175S (2009)ADSGoogle Scholar
  174. 174.
    Schnittman, J.D., Krolik, J.H.: X-ray polarization from accreting black holes: coronal emission. Astrophys. J. 712, 908S (2010)ADSGoogle Scholar
  175. 175.
    Schnittman, J.D., Angelini, L., Baring, M., et al.: X-ray polarization from black holes: GEMS scientific white paper (2013). arXiv:1301.1957S
  176. 176.
    Schnittman, J.D., Krolik, J.H., Noble, S.C.: X-ray spectra from magnetohydrodynamic simulations of accreting black holes. Astrophys. J. 769, 156 (2013)ADSGoogle Scholar
  177. 177.
    Shakura, N.I., Sunyaev, R.A.: Black holes in binary systems: observational appearance. Astron. Astrophys. 24, 337–355 (1973)ADSGoogle Scholar
  178. 178.
    Shafee, R., McClintock, J.E., Narayan, R., Davis, S.W., Li, L.-X., Remillard, R.A.: Estimating the spin of stellar-mass black holes by spectral fitting of the X-ray continuum. Astrophys. J. Lett. 636, L113 (2006)ADSGoogle Scholar
  179. 179.
    Shimura, T., Takahara, F.: On the spectral hardening factor of the X-ray emission from accretion disks in black hole candidates. Astrophys. J. 445, 780–788 (1995)ADSGoogle Scholar
  180. 180.
    Sotiriou, T.P., Limerati, S.: Theory of gravitation theories: a no-progress report. Int. J. Mod. Phys. D 17(3 & 4), 399–423 (2008)ADSMathSciNetzbMATHGoogle Scholar
  181. 181.
    Stefanov, I.Z.: Confronting models for the high-frequency QPOs with Lense–Thirring precession. Mon. Not. R. Astron. Soc. 444, 2178S (2014)ADSGoogle Scholar
  182. 182.
    Steiner, J.F., McClintock, J.E.: Modeling the jet kinematics of the black hole microquasar XTE J1550–564: a constraint on spin-orbit alignment. Astrophys. J. 745, 136 (2012)ADSGoogle Scholar
  183. 183.
    Steiner, J.F., McClintock, J.E., Orosz, J.A., Remillard, R.A., Bailyn, C.D., Kolehmainen, M., Straub, O.: The low-spin black hole in LMC X-3. Astrophys. J. Lett. 793, 29 (2014)ADSGoogle Scholar
  184. 184.
    Steiner, J.F., Reis, R.C., Fabian, A.C., et al.: A broad iron line in LMC X-1. Mon. Not. R. Astron. Soc. 427, 2552–2561 (2012)ADSGoogle Scholar
  185. 185.
    Steiner, J.F., Reis, R.C., McClintock, J.E., et al.: The spin of the black hole microquasar XTE J1550–564 via the continuum-fitting and Fe-line methods. Mon. Not. R. Astron. Soc. 416, 941 (2011)ADSGoogle Scholar
  186. 186.
    Stella, L., Vietri, M.: Lense-thirring precession and quasi-periodic oscillations in low-mass X-ray binaries. Astrophys. J. Lett. 492L, 59S (1998)ADSGoogle Scholar
  187. 187.
    Stella, L., Vietri, M., Morsink, S.M.: Correlations in the quasi-periodic oscillation frequencies of low-mass X-ray binaries and the relativistic precession model. Astrophys. J. Lett. 524L, 63S (1999)ADSGoogle Scholar
  188. 188.
    Shakura, N.I., Sunyaev, R.A.: Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355 (1973)ADSGoogle Scholar
  189. 189.
    Teukolsky, S.A.: The Kerr metric. Class. Quantum Gravity 32, 124006 (2015)ADSMathSciNetzbMATHGoogle Scholar
  190. 190.
    The Black Hole Imager
  191. 191.
    Thornburg, J.: Event and apparent horizon finders for \(3+1\) numerical relativity. Living Rev. Relativ. 10, 3 (2007).
  192. 192.
    Thorne, K.S., Will, C.M.: Theoretical frameworks for testing relativistic gravity. I. Foundations. Astrophys. J. 163, 595T (1971)ADSMathSciNetGoogle Scholar
  193. 193.
    Thorne, K.S., Price, R.H., MacDonald, D.A.: Black Holes, The Membrane Paradigm. Yale University Press, New Haven and London (1986)zbMATHGoogle Scholar
  194. 194.
    Tomsick, J.A., Nowak, M.A., Parker, M., et al.: The reflection component from Cygnus X-1 in the soft state measured by NuSTAR AND Suzaku. Astrophys. J. 780, 78 (2014)ADSGoogle Scholar
  195. 195.
    Tomsick, J.A., Parker, M.L., García, J.A., et al.: Alternative explanations for extreme supersolar iron abundances inferred from the energy spectrum of Cygnus X-1. Astrophys. J. 855, 3 (2018)ADSGoogle Scholar
  196. 196.
    Uttley, P., Cackett, E.M., Fabian, A.C., Kara, E., Wilkins, D.R.: X-ray reverberation around accreting black holes. Astron. Astrophys. Rev. 22, 72 (2014)ADSGoogle Scholar
  197. 197.
    Veledina, A., Poutanen, J., Ingram, A.: A unified lense-thirring precession model for optical and X-ray quasi-periodic oscillations in black hole binaries. Astrophys. J. 778, 165V (2013)ADSGoogle Scholar
  198. 198.
    van der Klis, M.: Rapid X-ray variability . In: Lewin, W., van der Klis, M. (eds.) Compact stellar X-ray sources. Cambridge Astrophysics Series, vol. 39, pp. 39–112. Cambridge University Press, Cambridge, UK. ISBN 978-0-521-82659-4, ISBN 0-521-82659-4 (2006).
  199. 199.
    Vigeland, S., Yunes, N., Stein, L.C.: Bumpy black holes in alternative theories of gravity. Phys. Rev. 83, 104027 (2011)Google Scholar
  200. 200.
    Walton, D.J., Reis, R.C., Cackett, E.M., Fabian, A.C., Miller, J.M.: The similarity of broad iron lines in X-ray binaries and active galactic nuclei. Mon. Not. R. Astron. Soc. 422, 2510W (2012)ADSGoogle Scholar
  201. 201.
    Walton, D.J., Tomsick, J.A., Madsen, K.K., et al.: The soft state of Cygnus X-1 observed with NuSTAR: a variable corona and a stable inner disk. Astrophys. J. 826, 87 (2016)ADSGoogle Scholar
  202. 202.
    Walton, D.J., Mooley, K., King, A.L., et al.: Living on a flare: relativistic reflection in V404 Cyg observed by NuSTAR during its summer 2015 outburst. Astrophys. J. 839, 110W (2017)ADSGoogle Scholar
  203. 203.
    Weisskopf, M.C., Ramsey, B., O’Dell, S., et al.: The imaging X-ray polarimetry explorer (IXPE). SPIE 9905E, 17W (2016)Google Scholar
  204. 204.
    Will, C.: The confrontation between general relativity and experiment. Living Rev. Relativ. 17, 4 (2014). ADSzbMATHGoogle Scholar
  205. 205.
    Wilms, Jörn, Reynolds, C.S., Begelman, M.C., Reeves, J., Molendi, S., Staubert, R., Kendziorra, E.: XMM-EPIC observation of MCG-6-30-15: direct evidence for the extraction of energy from a spinning black hole? Mon. Not. R. Astron. Soc. 328, 27 (2001)ADSGoogle Scholar
  206. 206.
    Wilkins, D.C.: Bound geodesics in the Kerr metric. Phys. Rev. D. 5, 814 (1974)ADSGoogle Scholar
  207. 207.
    Wilson-Hodge, C.A., Ray, P.S., Gendreau, K.: STROBE-X: X-ray timing and spectroscopy on dynamical timescales from microseconds to years. Res. Phys. 7, 3704W (2017)Google Scholar
  208. 208.
    Yunes, N., Siemens, S.: Gravitational-wave tests of general relativity with ground-based detectors and pulsar-timing arrays. Living Rev. Relativ. 16, 9 (2013).
  209. 209.
    Zhang, S.-N.: Black hole binaries and microquasars. Front. Phys. 8, 630Z (2013)Google Scholar
  210. 210.
    Zhang, S.-N., Cui, Wei, Chen, Wan: Black hole spin in X-ray binaries: observational consequences. Astrophys. J. Lett. 482L, 155Z (1997)ADSGoogle Scholar
  211. 211.
    Zhang, S.-N., Feroci, M., Santangelo, A.: eXTP: enhanced X-ray timing and polarimetry mission. Proc. SPIE 9905, 99051Q–1 (2016)Google Scholar
  212. 212.
    Zhu, Y., Davis, S.W., Narayan, R., et al.: The eye of the storm: light from the inner plunging region of black hole accretion discs. Mon. Not. R. Astron. Soc. 424, 2504 (2012)ADSGoogle Scholar
  213. 213.
    Zhuravlev, V.V., Ivanov, P.B.: A fully relativistic twisted disc around a slowly rotating Kerr black hole: derivation of dynamical equations and the shape of stationary configurations. Mon. Not. R. Astron. Soc. 415, 2122–2144 (2011)ADSGoogle Scholar
  214. 214.
    Zhuravlev, V.V., Ivanov, P.B., Fragile, P.C., Morales Teixeira, D.: No evidence for Bardeen–Petterson alignment in GRMHD simulations and semi-analytic models of moderately thin, prograde, tilted accretion disks. Astrophys. J. 796, 104 (2014)ADSGoogle Scholar

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Authors and Affiliations

  1. 1.Physics Department and the McDonnell Center for the Space SciencesWashington University in Saint LouisSaint LouisUSA

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