Probing the Strong (Stationary) Gravitational Field of Accreting Black Holes with X-ray Observations


High throughput time-resolved observations of accreting collapsed objects at X-ray energies provide key information on the motions of matter orbiting a few gravitational radii away from black holes. Predictions of general relativity in the strong field regime, such as relativistic epicyclic motions, precession, light bending and the presence and radius of an innermost stable circular orbit in the close vicinity of a black hole can be verified by making use of two powerful diagnostics, namely relativistically broadened \(\hbox {Fe-K}\alpha \) lines and variability on dynamical timescales, quasi periodic oscillations in particular. Moreover tomography and reverberation techniques relying upon combined spectral timing and polarimetric timing provide an entirely new perspective in the field. Both the low and high spacetime curvature regimes of gravity can be probed by studying black holes of vastly different masses in X-ray binaries and Active Galactic Nuclei, opening up the possibility of testing also some alternative theories of gravity. To achieve these goals, very large area X-ray instrumentation with good spectral resolution and polarimetric capability is required. Prospects and projects in this area of research are briefly surveyed.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11


  1. 1.

    Note that QPOs and relativistic Fe-lines are being studied also with the recently launched missions ASTROSAT [31] and NICER [33].

  2. 2.

    The Athena mission, with its \(\sim 1\) \(\hbox {m}^2\) X-ray optics, will also have reverberation capabilities though mainly in the energy range below \(\sim 10\) keV [44]. It is planned for launch in the 2030s.

  3. 3.

    To be launched in 2020.


  1. 1.

    Abbott, B.P., Abbott, R., Abbott, T.D., Abernathy, M.R., Acernese, F., Ackley, K., Adams, C., Adams, T., Addesso, P., Adhikari, R.X.: Tests of general relativity with GW150914. Phys. Rev. Lett. 116(22), 221101 (2016).

    ADS  Article  Google Scholar 

  2. 2.

    Bambi, C.: Probing the space-time geometry around black hole candidates with the resonance models for high-frequency QPOs and comparison with the continuum-fitting method. JCAP 9, 014 (2012).

    ADS  Article  Google Scholar 

  3. 3.

    Bambi, C.: Measuring the Kerr spin parameter of a non-Kerr compact object with the continuum-fitting and the iron line methods. JCAP 8, 055 (2013).

    ADS  Article  Google Scholar 

  4. 4.

    Belloni, T.M., Stella, L.: Fast variability from black-hole binaries. Space Sci. Rev. 183, 43–60 (2014).

    ADS  Article  Google Scholar 

  5. 5.

    de La Calle Pérez, I., Longinotti, A.L., Guainazzi, M., Bianchi, S., Dovčiak, M., Cappi, M., Matt, G., Miniutti, G., Petrucci, P.O., Piconcelli, E., Ponti, G., Porquet, D., Santos-Lleó, M.: FERO: finding extreme relativistic objects. I. Statistics of relativistic \(\text{ Fe } \text{ K }_{\alpha }\) lines in radio-quiet Type 1 AGN. Astron. Astrophys. 524, A50 (2010).

    Article  Google Scholar 

  6. 6.

    De Rosa, A., Uttley, P., Gou, L., Liu, Y., et al.: Accretion in Strong Field Gravity with eXTP. Sci. China Phys. Mech. Astron. (2018)

  7. 7.

    Dovčiak, M., Muleri, F., Goosmann, R.W., Karas, V., Matt, G.: Thermal disc emission from a rotating black hole: X-ray polarization signatures. MNRAS 391, 32–38 (2008).

    ADS  Article  Google Scholar 

  8. 8.

    Fabian, A.C.: The innermost extremes of black hole accretion. Astron. Nachr. 337, 375 (2016).

    ADS  Article  Google Scholar 

  9. 9.

    Fabian, A.C., Rees, M.J., Stella, L., White, N.E.: X-ray fluorescence from the inner disc in Cygnus X-1. MNRAS 238, 729–736 (1989).

    ADS  Article  Google Scholar 

  10. 10.

    Fabian, A.C., Vaughan, S., Nandra, K., Iwasawa, K., Ballantyne, D.R., Lee, J.C., De Rosa, A., Turner, A., Young, A.J.: A long hard look at MCG-6-30-15 with XMM-Newton. MNRAS 335, L1–L5 (2002).

    ADS  Article  Google Scholar 

  11. 11.

    Feroci, M., Bozzo, E., Brandt, S., Hernanz, M., van der Klis, M., Liu, L.P., Orleanski, P., Pohl, M., Santangelo, A., Schanne, S., et al.: The LOFT mission concept: a status update. In: Space Telescopes and Instrumentation 2016: Ultraviolet to Gamma Ray, Proc. SPIE , vol. 9905, p. 99051R (2016).

  12. 12.

    Feroci, M., Stella, L., Vacchi, A., Labanti, C., Rapisarda, M., et al.: LOFT: a large observatory for x-ray timing. In: Space telescopes and instrumentation 2010: ultraviolet to gamma ray, Proc. SPIE , vol. 7732, p. 77321V (2010).

  13. 13.

    Gierliński, M., Middleton, M., Ward, M., Done, C.: A periodicity of \(^{\sim }\)1hour in X-ray emission from the active galaxy RE J1034+396. Nature 455, 369–371 (2008).

    ADS  Article  Google Scholar 

  14. 14.

    Ingram, A., Done, C.: The effect of frame dragging on the iron K\(\alpha \) line in X-ray binaries. MNRAS 427, 934–947 (2012).

    ADS  Article  Google Scholar 

  15. 15.

    Ingram, A., Maccarone, T.J., Poutanen, J., Krawczynski, H.: Polarization modulation from lense-thirring precession in X-ray binaries. Astrophys. J. 807, 53 (2015).

    ADS  Article  Google Scholar 

  16. 16.

    Ingram, A., van der Klis, M., Middleton, M., Altamirano, D., Uttley, P.: Tomographic reflection modelling of quasi-periodic oscillations in the black hole binary H 1743–322. MNRAS 464, 2979–2991 (2017).

    ADS  Article  Google Scholar 

  17. 17.

    Ingram, A., van der Klis, M., Middleton, M., Done, C., Altamirano, D., Heil, L., Uttley, P., Axelsson, M.: A quasi-periodic modulation of the iron line centroid energy in the black hole binary H1743–322. MNRAS 461, 1967–1980 (2016).

    ADS  Article  Google Scholar 

  18. 18.

    Ingram, A.R., Maccarone, T.J.: An observational method for fast stochastic X-ray polarimetry timing. MNRAS 471, 4206–4217 (2017).

    ADS  Article  Google Scholar 

  19. 19.

    Iwasawa, K., Miniutti, G., Fabian, A.C.: Flux and energy modulation of redshifted iron emission in NGC 3516: implications for the black hole mass. MNRAS 355, 1073–1079 (2004).

    ADS  Article  Google Scholar 

  20. 20.

    Johannsen, T.: Systematic study of event horizons and pathologies of parametrically deformed Kerr spacetimes. Phys. Rev. D 87(12), 124017 (2013).

    ADS  Article  Google Scholar 

  21. 21.

    Johannsen, T.: X-ray probes of black hole accretion disks for testing the no-hair theorem. Phys. Rev. D 90(6), 064002 (2014).

    ADS  Article  Google Scholar 

  22. 22.

    Johannsen, T., Psaltis, D.: Testing the no-hair theorem with observations in the electromagnetic spectrum. I. Properties of a Quasi-Kerr spacetime. Astrophys. J. 716, 187–197 (2010).

    ADS  Article  Google Scholar 

  23. 23.

    Johannsen, T., Psaltis, D.: Testing the no-hair theorem with observations in the electromagnetic spectrum. III. Quasi-periodic variability. Astrophys. J. 726, 11 (2011).

    ADS  Article  Google Scholar 

  24. 24.

    Kara, E., Alston, W.N., Fabian, A.C., Cackett, E.M., Uttley, P., Reynolds, C.S., Zoghbi, A.: A global look at X-ray time lags in Seyfert galaxies. MNRAS 462, 511–531 (2016).

    ADS  Article  Google Scholar 

  25. 25.

    Kramer, M., Stairs, I.H., Manchester, R.N., McLaughlin, M.A., Lyne, A.G., Ferdman, R.D., Burgay, M., Lorimer, D.R., Possenti, A., D’Amico, N., Sarkissian, J.M., Hobbs, G.B., Reynolds, J.E., Freire, P.C.C., Camilo, F.: Tests of general relativity from timing the double pulsar. Science 314, 97–102 (2006).

    ADS  Article  Google Scholar 

  26. 26.

    LOFT Team: LOFT Assessment Study Report (Yellow Book): ESA/SRE 3, 1–108 (2013)

  27. 27.

    Maselli, A., Gualtieri, L., Pani, P., Stella, L., Ferrari, V.: Testing gravity with quasi-periodic oscillations from accreting black holes: the case of Einstein–Dilaton–Gauss–Bonnet theory. ApJ 801, 115 (2015).

    ADS  Article  Google Scholar 

  28. 28.

    Maselli, A., Pani, P., Cotesta, R., Gualtieri, L., Ferrari, V., Stella, L.: Geodesic models of quasi-periodic-oscillations as probes of quadratic gravity. Astrophys. J. 843, 25 (2017).

    ADS  Article  Google Scholar 

  29. 29.

    Miller, J.M., Fabian, A.C., Reynolds, C.S., Nowak, M.A., Homan, J., Freyberg, M.J., Ehle, M., Belloni, T., Wijnands, R., van der Klis, M., Charles, P.A., Lewin, W.H.G.: Evidence of black hole spin in GX 339–4: XMM-Newton/EPIC-pn and RXTE spectroscopy of the very high state. Astrophys. J. 606, L131–L134 (2004).

    ADS  Article  Google Scholar 

  30. 30.

    Motta, S.E., Belloni, T.M., Stella, L., Muñoz-Darias, T., Fender, R.: Precise mass and spin measurements for a stellar-mass black hole through X-ray timing: the case of GRO J1655–40. MNRAS 437, 2554–2565 (2014).

    ADS  Article  Google Scholar 

  31. 31.

    Padma, T.V.: Indian ASTROSAT telescope set for global stardom. Nature 525, 438–439 (2015).

    ADS  Article  Google Scholar 

  32. 32.

    Psaltis, D.: Probes and tests of strong-field gravity with observations in the electromagnetic spectrum. Living Rev. Relat. 11, 9 (2008).

    ADS  Article  MATH  Google Scholar 

  33. 33.

    Remillard, R.A., Cackett, E., Fabian, A.C., Miller, J.M., Ranga Reddy Pasham, D., Steiner, J.F.: Observations of Black Hole Binaries with NICER. In: AAS/High Energy Astrophysics Division #16, AAS/High Energy Astrophysics Division, vol. 16, p. 104.07 (2017)

  34. 34.

    Reynolds, C.S.: Measuring black hole spin using X-Ray reflection spectroscopy. Space Sci. Rev. 183, 277–294 (2014).

    ADS  Article  Google Scholar 

  35. 35.

    Ryan, F.D.: Gravitational waves from the inspiral of a compact object into a massive, axisymmetric body with arbitrary multipole moments. Phys. Rev. D 52, 5707–5718 (1995).

    ADS  Article  Google Scholar 

  36. 36.

    Stairs, I.H.: Testing general relativity with pulsar timing. Living Rev. Relat. 6, 5 (2003).

    ADS  Article  MATH  Google Scholar 

  37. 37.

    Stella, L.: Measuring black hole mass through variable line profiles from accretion disks. Nature 344, 747–749 (1990).

    ADS  Article  Google Scholar 

  38. 38.

    Stella, L., Vietri, M.: Lense-thirring precession and quasi-periodic oscillations in low-Mass X-Ray binaries. Astrophys. J. 492, L59–L62 (1998).

    ADS  Article  Google Scholar 

  39. 39.

    Stella, L., Vietri, M.: kHz Quasiperiodic oscillations in low-mass X-Ray binaries as probes of general relativity in the strong-field regime. Phys. Rev. Lett. 82, 17–20 (1999).

    ADS  Article  Google Scholar 

  40. 40.

    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. 524, L63–L66 (1999).

    ADS  Article  Google Scholar 

  41. 41.

    Syunyaev, R.A.: Variability of X-rays from black holes with accretion disks. Astrophys. J. 49, 1153 (1972)

    Google Scholar 

  42. 42.

    Tanaka, Y., Nandra, K., Fabian, A.C., Inoue, H., Otani, C., Dotani, T., Hayashida, K., Iwasawa, K., Kii, T., Kunieda, H., Makino, F., Matsuoka, M.: Gravitationally redshifted emission implying an accretion disk and massive black hole in the active galaxy MCG-6-30-15. Nature 375, 659–661 (1995).

    ADS  Article  Google Scholar 

  43. 43.

    Treves, A., Maraschi, L., Abramowicz, M.: Basic elements of the theory of accretion. PASP 100, 427–451 (1988).

    ADS  Article  Google Scholar 

  44. 44.

    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).

    ADS  Article  Google Scholar 

  45. 45.

    van der Klis, M.: Rapid X-ray variability. In: Lewin, W.H.G., van der Klis, M. (eds.) Compact Stellar X-ray Sources, pp. 39–112. Cambridge University Press, Cambridge (2006)

    Chapter  Google Scholar 

  46. 46.

    Weisskopf, M.C., Ramsey, B., O’Dell, S., Tennant, A., Elsner, R., Soffitta, P., Bellazzini, R., Costa, E., Kolodziejczak, J., Kaspi, V., Muleri, F., Marshall, H., Matt, G., Romani, R.: The Imaging X-ray Polarimetry Explorer (IXPE). In: Space Telescopes and Instrumentation 2016: Ultraviolet to Gamma Ray, Proc. SPIE , vol. 9905, p. 990517 (2016).

  47. 47.

    Wilson-Hodge, C.A., Ray, P.S., Gendreau, K., Chakrabarty, D., Feroci, M., Arzoumanian, Z., Brandt, S., Hernanz, M., Hui, C.M., Jenke, P.A., Maccarone, T., Remillard, R., Wood, K., Zane, S.: Strobe-X collaboration: STROBE-X: X-ray timing and spectroscopy on dynamical timescales from microseconds to years. Results Phys. 7, 3704–3705 (2017).

    ADS  Article  Google Scholar 

  48. 48.

    Zhang, S.N., Feroci, M., Santangelo, A., Dong, Y.W., Feng, H., Lu, F.J., Nandra, K., Wang, Z.S., Zhang, S., Bozzo, E., Brandt, S., De Rosa, A., Gou, L.J., Hernanz, M., van der Klis, M., et al.: eXTP: Enhanced X-ray Timing and Polarization mission. In: Space Telescopes and Instrumentation 2016: Ultraviolet to Gamma Ray, Proc. SPIE , vol. 9905, p. 99051Q (2016).

Download references


I acknowledge many useful discussions with and numerous inputs from members of the LOFT, eXTP and STROBE-X collaborations; I am especially indebted to Enrico Bozzo, Alessandra De Rosa, Marco Feroci, Adam Ingram, Michiel van der Klis, Leonardo Gualtieri, Andrea Maselli and Phil Uttley. Alessandra De Rosa provided also comments on an earlier version of this review. The author acknowledges financial contribution from ASI-INAF Agreement n.2017-14-H.O.

Author information



Corresponding author

Correspondence to Luigi Stella.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Stella, L. Probing the Strong (Stationary) Gravitational Field of Accreting Black Holes with X-ray Observations. Found Phys 48, 1500–1516 (2018).

Download citation


  • Tests of relativistic gravity
  • Black holes
  • Accretion disks
  • X-ray astronomy
  • Theories of gravity