Skip to main content
SpringerLink
Log in

Times of arrival (TOA) of signals in the Kerr-MOG black hole

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

Modified gravity (MOG) theories are alternatives to general relativity (GR) that arose primarily from the need to explain the observed galactic flat rotation curves without invoking the elusive dark matter hypothesized by GR. A well known MOG is the Scalar–Tensor–Vector–Gravity developed by Moffat, who has also found a spinning solution called the Kerr-MOG black hole (BH) characterized by the spin a and MOG parameter \(\alpha \), the latter determining the strength of the gravitational vector forces. We consider the static-MOG metric (\(a=0\)) to first understand how the nature of geometry drastically changes depending on different sectors of \(\alpha \). Then we study the influence of \(\alpha \) in each sector on a new astrophysical diagnostic caused by frame dragging, viz., the difference \(\varDelta t\) in the times of arrival at the observer of signals emanating from a variable pulsar (PSR) passing behind a Kerr-MOG lens in a PSR-BH binary system. The study generalizes the zeroth order Laguna–Wolszczan formula up to third PPN order in \(\left( 1/r\right) \) using thin-lens approximation, which reveals how \(\varDelta t\) is influenced both by a and \(\alpha \). The magnitude and sign of \(\alpha \) indicate deviations from GR (\(\alpha =0\)) and future measurements may constrain \(\alpha \) provided a suitable binary is identified.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. In contrast, there is also an effect of gravitational time advancement, proposed originally in [23], and some of its effects have been explored in [24, 25].

  2. The analogy is loose because the light rays do not travel in vacuum but in the weak gravitational field. For a true gravitational Bohm–Aharonov effect, see [26].

References

  1. Oort, J.: Some problems concerning the distribution of luminosities and peculiar velocities of extragalactic nebulae. Bull. Astron. Inst. Neth. 6, 155 (1931)

    ADS  MATH  Google Scholar 

  2. Riess, A.G., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  3. Perlmutter, S., et al.: Discovery of a supernova explosion at half the age of the Universe. Nature (London) 391, 51 (1998)

    Article  ADS  Google Scholar 

  4. Agnese, R., et al.: (SuperCDMS Collaboration): search for low-mass weakly interacting massive particles with SuperCDMS. Phys. Rev. Lett. 112, 241302 (2014)

    Article  ADS  Google Scholar 

  5. Mannheim, P.D., O’Brien, J.G.: Impact of a global quadratic potential on galactic rotation curves. Phys. Rev. Lett. 106, 121101 (2011)

    Article  ADS  Google Scholar 

  6. Nandi, K.K., Bhadra, A.: Comment on “Impact of a Global Quadratic Potential on Galactic Rotation Curves”. Phys. Rev. Lett. 109, 079001 (2012)

    Article  ADS  Google Scholar 

  7. Milgrom, M.: A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophys. J. 270, 365 (1983)

    Article  ADS  Google Scholar 

  8. Nojiri, S., Odintsov, S.D.: Modified \(f(R)\) gravity consistent with realistic cosmology: from a matter dominated epoch to a dark energy universe. Phys. Rev. D 74, 086005 (2006)

    Article  ADS  Google Scholar 

  9. Moffat, J.W.: Scalar–tensor–vector gravity theory. J. Cosmol. Astropart. Phys. 03, 004 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Izmailov, R.N., et al.: Modified gravity black hole lensing observables in weak and strong field of gravity. Mon. Not. R. Astron. Soc. 483, 3754 (2019)

    Article  ADS  Google Scholar 

  11. Brownstein, J.R., Moffat, J.W.: Galaxy rotation curves without nonbaryonic dark matter. Astrophys. J. 636, 721 (2006)

    Article  ADS  Google Scholar 

  12. Brownstein, J.R., Moffat, J.W.: Galaxy cluster masses without non-baryonic dark matter. Mon. Not. R. Astron. Soc. 367, 527 (2006)

    Article  ADS  Google Scholar 

  13. Moffat, J.W., Rahvar, S.: The MOG weak field approximation and observational test of galaxy rotation curves. Mon. Not. R. Astron. Soc. 436, 1439 (2013)

    Article  ADS  Google Scholar 

  14. Pérez, D., Armengol, F.G.L., Romero, G.E.: Accretion disks around black holes in scalar–tensor–vector gravity. Phys. Rev. D 95, 104047 (2017)

    Article  ADS  Google Scholar 

  15. Lopez Armengol, F.G., Romero, G.E.: Neutron stars in scalar–tensor–vector gravity. Gen. Relativ. Gravit. 49, 27 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Brownstein, J.R., Moffat, J.W.: The Bullet Cluster 1E0657-558 evidence shows modified gravity in the absence of dark matter. Mon. Not. R. Astron. Soc. 382, 29 (2007)

    Article  ADS  Google Scholar 

  17. Moffat, J.W., Toth, V.T.: Testing Modified Gravity with Globular Cluster Velocity Dispersions. Astrophys. J. 680, 1158 (2008)

    Article  ADS  Google Scholar 

  18. Moffat, J.W., Toth, V.T.: Cosmological observations in a modified theory of gravity (MOG). Galaxies 1, 65 (2013)

    Article  ADS  Google Scholar 

  19. Moffat, J.W., Toth, V.T.: Rotational velocity curves in the Milky Way as a test of modified gravity. Phys. Rev. D 91, 043004 (2015)

    Article  ADS  Google Scholar 

  20. Moffat, J.W., Rahvar, S.: The MOG weak field approximation: II. Observational test of Chandra X-ray clusters. Mon. Not. R. Astron. Soc. 441, 3724 (2014)

    Article  ADS  Google Scholar 

  21. Moffat, J.W.: Black holes in modified gravity (MOG). Eur. Phys. J. C 75, 175 (2015)

    Article  ADS  Google Scholar 

  22. Moffat, J.W.: Modified gravity black holes and their observable shadows. Eur. Phys. J. C 75, 130 (2015)

    Article  ADS  Google Scholar 

  23. Bhadra, A., Nandi, K.K.: Gravitational time advancement and its possible detection. Gen. Relat. Grav. 42, 293 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Deng, X.-M., Xie, Y.: Gravitational time advancement under gravity’s rainbow. Phys. Lett. B 772, 152 (2017)

    Article  ADS  MATH  Google Scholar 

  25. Ghosh, S., Bhadra, A.: Influences of dark energy and dark matter on gravitational time advancement. Eur. Phys. J. C 75, 494 (2015)

    Article  ADS  Google Scholar 

  26. Ford, L.H., Vilenkin, A.: A gravitational analogue of the Aharonov–Bohm effect. J. Phys. A Math. Gen. 14, 2353 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  27. Laguna, P., Wolszczan, A.: Pulse arrival times from binary pulsars with rotating black hole companions. Astrophys. J. 486, L27 (1997)

    Article  ADS  Google Scholar 

  28. Datta, B., Kapoor, R.C.: General relativistic effects on the pulse profile of fast pulsars. Nature 315, 557 (1985)

    Article  ADS  Google Scholar 

  29. Matilsky, T., Shräder, C., Tananbaum, H.: Evidence for 200 second variability in the X-ray flux of the quasar 1525 + 227. Astrophys. J. 258, L1 (1982)

    Article  ADS  Google Scholar 

  30. Izmailov, R.N., et al.: Relative time delay in a spinning black hole as a diagnostic for no-hair theorem. Eur. Phys. J. C 79, 105 (2019)

    Article  ADS  Google Scholar 

  31. Penrose, R.: Gravitional collapse: the role of general relativity. Riv. Nuovo Cimento 1, 252 (1969)

    Google Scholar 

  32. Izmailov, R.N., Karimov, RKh, Potapov, A.A., Nandi, K.K.: String effect on the relative time delay in the Kerr–Sen black hole. Ann. Phys. 413, 168069 (2020)

    Article  MathSciNet  Google Scholar 

  33. Karimov, RKh, Izmailov, R.N., Potapov, A.A., Nandi, K.K.: Terrestrial Sagnac delay constraining modified gravity models. Gen. Relativ. Gravit. 50, 44 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. Hartle, J.B.: Gravity: An Introduction to Elnstein’s General Relativity. Pearson Inc., San Francisco (2003)

    Google Scholar 

  35. Manko, V.S., Novikov, I.D.: Generalizations of the Kerr and Kerr–Newman metrics possessing an arbitrary set of mass-multipole moments. Class. Quantum Grav. 9, 2477 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Glampedakis, K., Babak, S.: Mapping spacetimes with LISA: inspiral of a test body in a ‘quasi-Kerr’ field. Class. Quantum Grav. 23, 4167 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Dadhich, N., Maartens, R., Papadopoulos, P., Rezania, V.: Black holes on the brane. Phys. Lett. B 487, 1 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Keeton, C.R., Petters, A.O.: Formalism for testing theories of gravity using lensing by compact objects. II. Probing post-post-Newtonian metrics. Phys. Rev. D 73, 044024 (2006)

    Article  ADS  Google Scholar 

  39. Nandi, K.K., et al.: Features of galactic halo in a brane world model and observationalconstraints. Mon. Not. R. Astron. Soc. 399, 2079 (2009)

    Article  ADS  Google Scholar 

  40. Boyer, R.H., Lindquist, R.W.: Maximal analytic extension of the Kerr Metric. J. Math. Phys. 8, 265 (1967)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Dymnikova, I.G.: Motion of particles and photons in the gravitational field of a rotating body (In memory of Vladimir Afanas’evich Ruban). Sov. Phys. Uspekhi 29, 215 (1986)

    Article  ADS  Google Scholar 

  42. Bozza, V.: Gravitational lensing in the strong field limit. Phys. Rev. D 66, 103001 (2002)

    Article  ADS  Google Scholar 

  43. Sasaki, M., Shiromizu, T., Maeda, K-i: Gravity, stability, and energy conservation on the Randall–Sundrum brane world. Phys. Rev. D 62, 024008 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  44. Lipunov, V.M., Bogomazov, A.I., Abubekerov, M.K.: How abundant is the population of binary radio pulsars with black holes? Mon. Not. R. Astron. Soc. 359, 1517 (2005)

    Article  ADS  Google Scholar 

  45. Gou, L., et al.: The extreme spin of the black hole in Cygnus X-1. Astrophys. J. 742, 85 (2011)

    Article  ADS  Google Scholar 

  46. Pfahl, E., Loeb, A.: Probing the spacetime around Sagittarius A* with radio pulsars. Astrophys. J. 615, 253 (2004)

    Article  ADS  Google Scholar 

  47. Faucher-Giguère, C.A., Loeb, A.: Pulsar-black hole binaries in the Galactic Centre. Mon. Not. R. Astron. Soc. 415, 3951 (2011)

    Article  ADS  Google Scholar 

  48. Kato, Y., Miyoshi, M., Takahashi, R., Negoro, H., Matsumoto, R.: Measuring spin of a supermassive black hole at the Galactic centre—implications for a unique spin. Mon. Not. R. Astron. Soc. 403, L74 (2010)

    Article  ADS  Google Scholar 

  49. Van Straten, W., et al.: A test of general relativity from the three-dimensional orbital geometry of a binary pulsar. Nature (London) 412, 158 (2001)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The reported study was funded by RFBR according to the research Project No. 18-32-00377.

Author information

Authors and Affiliations

  1. Zel’dovich International Center for Astrophysics, M. Akmullah Bashkir State Pedagogical University, 3A, October Revolution Street, Ufa, RB, Russia, 450008

    G. Y. Tuleganova, R. N. Izmailov, R. Kh. Karimov & K. K. Nandi

  2. Department of Physics and Astronomy, Bashkir State University, 47A, Lenin Street, Sterlitamak, RB, Russia, 453103

    A. A. Potapov & K. K. Nandi

  3. High Energy Cosmic Ray Research Center, University of North Bengal, Darjeeling, WB, 734 013, India

    K. K. Nandi

Authors
  1. G. Y. Tuleganova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. N. Izmailov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Kh. Karimov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. A. Potapov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. K. K. Nandi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. N. Izmailov.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tuleganova, G.Y., Izmailov, R.N., Karimov, R.K. et al. Times of arrival (TOA) of signals in the Kerr-MOG black hole. Gen Relativ Gravit 52, 31 (2020). https://doi.org/10.1007/s10714-020-02684-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-020-02684-0

Keywords

Search

Navigation