Skip to main content
SpringerLink
Log in
Book cover

Black Holes: A Laboratory for Testing Strong Gravity pp 287–303Cite as

Tests with Other Approaches

  • Chapter
  • First Online:

  • 1180 Accesses

Abstract

The chapter briefly reviews current/future attempts to test the Kerr metric around astrophysical black holes with SgrA\(^{*}\), precise measurements in the weak gravitational field of black holes, and with gravitational waves.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    http://www.eventhorizontelescope.org/.

  2. 2.

    The expansion in multipole moments is also possible when the spacetime is not axisymmetric, but in this case the mass and the current moments of order \(\ell \) are tensors. If the spacetime is axisymmetric, there are some simplifications, and the mass and the current moments of any order \(\ell \) are completely determined by two scalars, namely \(M_\ell \) and \(S_\ell \). In the case of tests of the Kerr metric in the weak field, it is common to assume that the spacetime is axisymmetric, because it sounds a physically plausible hypothesis and simplifies the problem. Let us also note that some assumptions may not hold in some relevant cases. For instance, black hole solutions in alternative theories of gravity may not be Ricci-flat, and an example is the case of black holes in Einstein–dilaton–Gauss–Bonnet gravity of Sect. 12.1.2. The analyticity assumption may also not hold, as in the case of the presence of a massive scalar field with a Yukawa type solution.

References

  1. B.P. Abbott et al., LIGO Scientific and Virgo Collaborations. Phys. Rev. Lett. 116, 061102 (2016), arXiv:1602.03837 [gr-qc]

  2. B.P. Abbott et al., LIGO Scientific and Virgo Collaborations. Phys. Rev. Lett. 116, 221101 (2016), arXiv:1602.03841 [gr-qc]

  3. B.P. Abbott et al., LIGO Scientific and Virgo Collaborations. Phys. Rev. Lett. 116, 241103 (2016), arXiv:1606.04855 [gr-qc]

  4. A. Abdujabbarov, F. Atamurotov, Y. Kucukakca, B. Ahmedov, U. Camci, Astrophys. Space Sci. 344, 429 (2013), arXiv:1212.4949 [physics.gen-ph]

  5. A. Abdujabbarov, M. Amir, B. Ahmedov, S.G. Ghosh, Phys. Rev. D 93, 104004 (2016), arXiv:1604.03809 [gr-qc]

  6. L. Amarilla, E.F. Eiroa, Phys. Rev. D 85, 064019 (2012), arXiv:1112.6349 [gr-qc]

  7. L. Amarilla, E.F. Eiroa, Phys. Rev. D 87, 044057 (2013), arXiv:1301.0532 [gr-qc]

  8. L. Amarilla, E.F. Eiroa, G. Giribet, Phys. Rev. D 81, 124045 (2010), arXiv:1005.0607 [gr-qc]

  9. R. Angelil, P. Saha, D. Merritt, Astrophys. J. 720, 1303 (2010), arXiv:1007.0007 [astro-ph.GA]

  10. K.G. Arun, B.R. Iyer, M.S.S. Qusailah, B.S. Sathyaprakash, Class. Quantum Gravity 23, L37 (2006), arXiv:gr-qc/0604018

  11. K.G. Arun, B.R. Iyer, M.S.S. Qusailah, B.S. Sathyaprakash, Phys. Rev. D 74, 024006 (2006), arXiv:gr-qc/0604067

  12. F. Atamurotov, A. Abdujabbarov, B. Ahmedov, Astrophys. Space Sci. 348, 179 (2013)

    Google Scholar 

  13. F. Atamurotov, A. Abdujabbarov, B. Ahmedov, Phys. Rev. D 88, 064004 (2013)

    Google Scholar 

  14. C. Bambi, Phys. Rev. D 87, 107501 (2013), arXiv:1304.5691 [gr-qc]

  15. C. Bambi, Class. Quantum Gravity 32, 065005 (2015), arXiv:1409.0310 [gr-qc]

  16. C. Bambi, K. Freese, Phys. Rev. D 79, 043002 (2009), arXiv:0812.1328 [astro-ph]

  17. C. Bambi, N. Yoshida, Class. Quantum Gravity 27, 205006 (2010), arXiv:1004.3149 [gr-qc]

  18. C. Bambi, F. Caravelli, L. Modesto, Phys. Lett. B 711, 10 (2012), arXiv:1110.2768 [gr-qc]

  19. L. Barack, Class. Quantum Gravity 26, 213001 (2009), arXiv:0908.1664 [gr-qc]

  20. L. Barack, C. Cutler, Phys. Rev. D 75, 042003 (2007), arXiv:gr-qc/0612029

  21. E. Berti, V. Cardoso, Int. J. Mod. Phys. D 15, 2209 (2006), arXiv:gr-qc/0605101

  22. E. Berti, V. Cardoso, C.M. Will, Phys. Rev. D 73, 064030 (2006), arXiv:gr-qc/0512160

  23. P. Canizares, J.R. Gair, C.F. Sopuerta, Phys. Rev. D 86, 044010 (2012), arXiv:1205.1253 [gr-qc]

  24. V. Cardoso, E. Franzin, P. Pani, Phys. Rev. Lett. 116, 171101 (2016) (Erratum: Phys. Rev. Lett. 117, 089902 (2016)), arXiv:1602.07309 [gr-qc]

  25. J. Chennamangalam, D.R. Lorimer, Mon. Not. R. Astron. Soc. 440, 86 (2014), arXiv:1311.4846 [astro-ph.HE]

  26. C.B.M.H. Chirenti, L. Rezzolla, Class. Quantum Gravity 24, 4191 (2007), arXiv:0706.1513 [gr-qc]

  27. C. Chirenti, L. Rezzolla, arXiv:1602.08759 [gr-qc]

  28. N. Cornish, L. Sampson, N. Yunes, F. Pretorius, Phys. Rev. D 84, 062003 (2011), arXiv:1105.2088 [gr-qc]

  29. P.V.P. Cunha, C.A.R. Herdeiro, E. Radu, H.F. Runarsson, Phys. Rev. Lett. 115, 211102 (2015), arXiv:1509.00021 [gr-qc]

  30. P.V.P. Cunha, C.A.R. Herdeiro, E. Radu, H.F. Runarsson, Int. J. Mod. Phys. D 25, 1641021 (2016), arXiv:1605.08293 [gr-qc]

  31. J.P. De Villiers, J.F. Hawley, J.H. Krolik, Astrophys. J. 599, 1238 (2003), arXiv:astro-ph/0307260

  32. K. Dodds-Eden, P. Sharma, E. Quataert, R. Genzel, S. Gillessen, F. Eisenhauer, D. Porquet, Astrophys. J. 725, 450 (2010), arXiv:1005.0389 [astro-ph.GA]

  33. S. Doeleman et al., Nature 455, 78 (2008), arXiv:0809.2442 [astro-ph]

  34. O. Dreyer, B.J. Kelly, B. Krishnan, L.S. Finn, D. Garrison, R. Lopez-Aleman, Class. Quantum Gravity 21, 787 (2004), arXiv:gr-qc/0309007

  35. F. Eisenhauer et al., Proc. SPIE Int. Soc. Opt. Eng. 7013, 2A (2008), arXiv:0808.0063 [astro-ph]

  36. V.L. Fish et al., Astrophys. J. 727, L36 (2011), arXiv:1011.2472 [astro-ph.GA]

  37. V.L. Fish et al., Astrophys. J. 820, 90 (2016), arXiv:1602.05527 [astro-ph.GA]

  38. J.R. Gair, M. Vallisneri, S.L. Larson, J.G. Baker, Living Rev. Relativ. 16, 7 (2013), arXiv:1212.5575 [gr-qc]

  39. R. Genzel, R. Schödel, T. Ott, A. Eckart, T. Alexander, F. Lacombe, D. Rouan, B. Aschenbach, Nature 425, 934 (2003), arXiv:astro-ph/0310821

  40. R.P. Geroch, J. Math. Phys. 11, 2580 (1970)

    Google Scholar 

  41. M. Ghasemi-Nodehi, Z. Li, C. Bambi, Eur. Phys. J. C 75, 315 (2015), arXiv:1506.02627 [gr-qc]

  42. K. Glampedakis, S. Babak, Class. Quantum Gravity 23, 4167 (2006), arXiv:gr-qc/0510057

  43. S. Gossan, J. Veitch, B.S. Sathyaprakash, Phys. Rev. D 85, 124056 (2012), arXiv:1111.5819 [gr-qc]

  44. N. Hamaus, T. Paumard, T. Muller, S. Gillessen, F. Eisenhauer, S. Trippe, R. Genzel, Astrophys. J. 692, 902 (2009), arXiv:0810.4947 [astro-ph]

  45. R.O. Hansen, J. Math. Phys. 15, 46 (1974)

    Google Scholar 

  46. T. Johannsen, D. Psaltis, Astrophys. J. 718, 446 (2010), arXiv:1005.1931 [astro-ph.HE]

  47. T. Johannsen, C. Wang, A.E. Broderick, S.S. Doeleman, V.L. Fish, A. Loeb, D. Psaltis, Phys. Rev. Lett. 117, 091101 (2016), arXiv:1608.03593 [astro-ph.HE]

  48. R. Konoplya, A. Zhidenko, Phys. Lett. B 756, 350 (2016), arXiv:1602.04738 [gr-qc]

  49. H.J. Lehto, M.J. Valtonen, Astrophys. J. 460, 207 (1996)

    Google Scholar 

  50. Z. Li, C. Bambi, JCAP 1401, 041 (2014), arXiv:1309.1606 [gr-qc]

  51. Z. Li, C. Bambi, Phys. Rev. D 90, 024071 (2014), arXiv:1405.1883 [gr-qc]

  52. Z. Li, L. Kong, C. Bambi, Astrophys. J. 787, 152 (2014), arXiv:1401.1282 [gr-qc]

  53. N. Lin, Z. Li, J. Arthur, R. Asquith, C. Bambi, JCAP 1509, 038 (2015), arXiv:1505.05329 [gr-qc]

  54. D. Liu, Z. Li, C. Bambi, JCAP 1501, 020 (2015), arXiv:1411.2329 [gr-qc]

  55. K. Liu, N. Wex, M. Kramer, J.M. Cordes, T.J.W. Lazio, Astrophys. J. 747, 1 (2012), arXiv:1112.2151 [astro-ph.HE]

  56. D.R. Lorimer, M. Kramer, Handbook of Pulsar Astronomy (Cambridge University Press, Cambridge, 2005)

    Google Scholar 

  57. S. Markoff, H. Falcke, F. Yuan, P.L. Biermann, Astron. Astrophys. 379, L13 (2001), arXiv:astro-ph/0109081

  58. D. Merritt, T. Alexander, S. Mikkola, C.M. Will, Phys. Rev. D 81, 062002 (2010), arXiv:0911.4718 [astro-ph.GA]

  59. P. Pani, E. Berti, V. Cardoso, Y. Chen, R. Norte, Phys. Rev. D 80, 124047 (2009), arXiv:0909.0287 [gr-qc]

  60. P. Pani, V. Cardoso, L. Gualtieri, Phys. Rev. D 83, 104048 (2011), arXiv:1104.1183 [gr-qc]

  61. E. Poisson, A. Pound, I. Vega, Living Rev. Relativ. 14, 7 (2011), arXiv:1102.0529 [gr-qc]

  62. F.D. Ryan, Phys. Rev. D 52, 5707 (1995)

    Google Scholar 

  63. J. Schee, Z. Stuchlik, Int. J. Mod. Phys. D 18, 983 (2009), arXiv:0810.4445 [astro-ph]

  64. C.F. Sopuerta, N. Yunes, Phys. Rev. D 80, 064006 (2009), arXiv:0904.4501 [gr-qc]

  65. O. Straub, F.H. Vincent, M.A. Abramowicz, E. Gourgoulhon, T. Paumard, Astron. Astrophys. 543, A83 (2012), arXiv:1203.2618 [astro-ph.GA]

  66. M. Tagger, F. Melia, Astrophys. J. 636, L33 (2006), arXiv:astro-ph/0511520

  67. G. Trap et al., Astron. Astrophys. 528, A140 (2011), arXiv:1102.0192 [astro-ph.HE]

  68. S. Trippe, T. Paumard, T. Ott, S. Gillessen, F. Eisenhauer, F. Martins, R. Genzel, Mon. Not. R. Astron. Soc. 375, 764 (2007), arXiv:astro-ph/0611737

  69. N. Tsukamoto, Z. Li, C. Bambi, JCAP 1406, 043 (2014), arXiv:1403.0371 [gr-qc]

  70. M.J. Valtonen et al., Astrophys. J. 709, 725 (2010), arXiv:0912.1209 [astro-ph.HE]

  71. M.J. Valtonen, S. Mikkola, H.J. Lehto, A. Gopakumar, R. Hudec, J. Polednikova, Astrophys. J. 742, 22 (2011), arXiv:1108.5861 [astro-ph.CO]

  72. F.H. Vincent, W. Yan, M.A. Abramowicz, A.A. Zdziarski, O. Straub, Astron. Astrophys. 574, A48 (2015), arXiv:1406.0353 [astro-ph.GA]

  73. S.W. Wei, Y.X. Liu, JCAP 1311, 063 (2013), arXiv:1311.4251 [gr-qc]

  74. S.W. Wei, P. Cheng, Y. Zhong, X.N. Zhou, JCAP 1508, 004 (2015), arXiv:1501.06298 [gr-qc]

  75. N. Wex, S. Kopeikin, Astrophys. J. 514, 388 (1999), arXiv:astro-ph/9811052

  76. C.M. Will, Phys. Rev. D 50, 6058 (1994), arXiv:gr-qc/9406022

  77. C.M. Will, Astrophys. J. 674, L25 (2008), arXiv:0711.1677 [astro-ph]

  78. K. Yagi, L.C. Stein, Class. Quantum Gravity 33, 054001 (2016), arXiv:1602.02413 [gr-qc]

  79. K. Yagi, L.C. Stein, N. Yunes, T. Tanaka, Phys. Rev. D 85, 064022 (2012) (Erratum: Phys. Rev. D 93, 029902 (2016)), arXiv:1110.5950 [gr-qc]

  80. K. Yagi, N. Yunes, T. Tanaka, Phys. Rev. Lett. 109, 251105 (2012) (Erratum: Phys. Rev. Lett. 116, 169902 (2016)), arXiv:1208.5102 [gr-qc]

  81. F. Yuan, R. Narayan, Annu. Rev. Astron. Astrophys. 52, 529 (2014), arXiv:1401.0586 [astro-ph.HE]

  82. N. Yunes, F. Pretorius, Phys. Rev. D 80, 122003 (2009), arXiv:0909.3328 [gr-qc]

  83. N. Yunes, X. Siemens, Living Rev. Relativ. 16, 9 (2013), arXiv:1304.3473 [gr-qc]

  84. N. Yunes, K. Yagi, F. Pretorius, arXiv:1603.08955 [gr-qc]

  85. F. Yusef-Zadeh, D. Roberts, M. Wardle, C.O. Heinke, G.C. Bower, Astrophys. J. 650, 189 (2006), arXiv:astro-ph/0603685

  86. F. Zhang, Y. Lu, Q. Yu, Astrophys. J. 809, 127 (2015), arXiv:1508.06293 [astro-ph.HE]

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Fudan University, Shanghai, China

    Cosimo Bambi

  2. Theoretical Astrophysics, Eberhard-Karls Universität Tübingen, Tübingen, Germany

    Cosimo Bambi

Authors
  1. Cosimo Bambi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cosimo Bambi .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Nature Singapore Pte Ltd.

About this chapter

Cite this chapter

Bambi, C. (2017). Tests with Other Approaches. In: Black Holes: A Laboratory for Testing Strong Gravity. Springer, Singapore. https://doi.org/10.1007/978-981-10-4524-0_14

Download citation

Publish with us

Policies and ethics

Search

Navigation