Twisting of light around rotating black holes

Journal name:
Nature Physics
Volume:
7,
Pages:
195–197
Year published:
DOI:
doi:10.1038/nphys1907
Received
Accepted
Published online

Kerr black holes are among the most intriguing predictions of Einstein’s general relativity theory1, 2. These rotating massive astrophysical objects drag and intermix their surrounding space and time, deflecting and phase-modifying light emitted near them. We have found that this leads to a new relativistic effect that imprints orbital angular momentum on such light. Numerical experiments, based on the integration of the null geodesic equations of light from orbiting point-like sources in the Kerr black hole equatorial plane to an asymptotic observer3, indeed identify the phase change and wavefront warping and predict the associated light-beam orbital angular momentum spectra4. Setting up the best existing telescopes properly, it should be possible to detect and measure this twisted light, thus allowing a direct observational demonstration of the existence of rotating black holes. As non-rotating objects are more an exception than a rule in the Universe, our findings are of fundamental importance.

At a glance

Figures

  1. Total phase variation of light generated in a region of size 100RS[times]100RS in the equatorial xy plane of a quasi-extremal rotating black hole (a=0.99) as seen by an asymptotic observer.
    Figure 1: Total phase variation of light generated in a region of size 100RS×100RS in the equatorial xy plane of a quasi-extremal rotating black hole (a=0.99) as seen by an asymptotic observer.

    This region of the sky shows what would be observed with a telescope if the black hole rotation axis is inclined an angle i=45° relative to the observer. The total phase variation includes the anamorphic effect due to both the spacetime curvature and the inclination of the disk. The corresponding OAM spectral distribution is quite complex (inset), with two strong peaks at =−2 and =1, and extends towards higher OAM modes with a rapid fall-off.

  2. Phase variation of photons as measured by an asymptotic observer.
    Figure 2: Phase variation of photons as measured by an asymptotic observer.

    The xy plane represents a 100×100 Schwarzschild radii large region of the sky centred on the KBH. a,c, The OAM acquired due only to the KBH rotation for a=0.99 (a) and a=0.5 (c), normalized to the field of a quasi-static black hole (a=0.01). Here we estimate the torsion of the optical path due to the spacetime dragging of the KBH. The spacetime dragging effect of the extremal KBH (a=0.99) results in a wide, bimodal OAM power spectrum distribution peaked at =−1 and =1 relative to a static BH. In contrast, for a KBH with a=0.5, the only significant contribution is a narrow OAM spectrum that comes from the immediate neighbourhood of the compact object where the relativistic effects are strongest. The torsion is zero if the black hole is static, in agreement with ref. 9. b,d, The OAM spectra of the cases a and c, respectively. Whereas the OAM spectrum in b has its maximum power in the =−1 mode, the strongest mode in d is =0, and the powers in all of the modes are plotted relative to this mode. As the =0 mode has (relative) power 1, it is greyed out to indicate that it goes off scale.

References

  1. Chandrasekhar, S. The Mathematical Theory of Black Holes (Oxford Univ. Press, 1992).
  2. Bozza, V. Gravitational lensing by black holes. Gen. Rel. Grav. 42, 22692300 (2010).
  3. Ćadež, A. & Calvani, M. Relativistic emission lines from accretion disks around black holes. Mon. Not. R. Astron. Soc. 363, 177182 (2005).
  4. Torner, L., Torres, J. & Carrasco, S. Digital spiral imaging. Opt. Express 13, 873881 (2005).
  5. Dehnen, H. Gravitational Faraday-effect. Int. J. Theor. Phys. 7, 467474 (1973).
  6. Molina-Terriza, G., Torres, J. P. & Torner, L. Twisted photons. Nature Phys. 3, 305310 (2007).
  7. Beckwith, K. & Done, C. Extreme gravitational lensing near rotating black holes. Mon. Not. R. Astron. Soc. 359, 12171228 (2005).
  8. Carini, P., Long-Long, F., Miao, L. & Ruffini, R. Phase evolution of the photon in Kerr spacetime. Phys. Rev. D 46, 54075413 (1992).
  9. Long-Long, F. & Wo-Lung, L. Gravitomagnetism and the Berry phase of photon in a rotating gravitational field. Int. J. Mod. Phys. D 10, 961969 (2001).
  10. Marucci, L., Manzo, C. & Paparo, D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. 96, 163905 (2006).
  11. Grier, D. G. A revolution in optical manipulation. Nature 424, 810816 (2003).
  12. Gibson, G. et al. Free-space information transfer using light beams carrying orbital angular momentum. Opt. Express 12, 54485456 (2004).
  13. Thidé, B. et al. Utilization of photon orbital angular momentum in the low-frequency radio domain. Phys. Rev. Lett. 99, 087701 (2007).
  14. Harwit, M. Photon orbital angular momentum in astrophysics. Astrophys. J. 597, 12661270 (2003).
  15. Elias, N. M. II Photon orbital angular momentum in astronomy. Astron. Astrophys. 492, 883922 (2008).
  16. Tamburini, F., Anzolin, G., Bianchini, A. & Barbieri, C. Overcoming the Rayleigh criterion limit with optical vortices. Phys. Rev. Lett. 97, 163903 (2006).
  17. Serabyn, E., Mawet, D. & Burruss, R. An image of an exoplanet separated by two diffraction beamwidths from a star. Nature 464, 10181020 (2010).
  18. Anzolin, G., Tamburini, F., Bianchini, A., Umbriaco, G. & Barbieri, C. Optical vortices with star light. Astron. Astrophys. 488, 11591165 (2008).
  19. Berestetskii, V. B., Lifshitz, E. M. & Pitaevskii, L. P. Quantum Electrodynamics 2nd edn,Vol. 4 (Butterworth-Heinemann, 1982).
  20. Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313316 (2001).
  21. Leach, J., Padgett, M. J., Barnett, S. M., Franke-Arnold, S. & Courtial, J. Measuring the orbital angular momentum of a single photon. Phys. Rev. Lett. 88, 257901 (2002).
  22. Tamburini, F. & Vicino, D. Photon wave function: A covariant formulation and equivalence with QED. Phys. Rev. A 78, 052116 (2008).
  23. Falcke, H., Melia, F. & Agol, E. Viewing the shadow of the black hole at the Galactic Center. Astrophys. J. 528, L13L16 (2000).
  24. Genzel, R. et al. Near-infrared flares from accreting gas around the supermassive black hole at the Galactic Centre. Nature 425, 934937 (2003).
  25. Aschenbach, B., Grosso, N., Porquet, D. & Predehl, P. X-ray flares reveal mass and angular momentum of the Galactic Center black hole. Astron. Astrophys. 417, 7178 (2004).
  26. Broderick, A. E., Fish, V. L., Doeleman, S. S. & Loeb, A. Estimating the parameters of Sagittarius A*’s accretion flow via millimeter VLBI. Astrophys. J. 697, 4554 (2009).
  27. Tamburini, F., Sponselli, A., Thidé, B. & Mendonça, J. T. Photon orbital angular momentum and mass in a plasma vortex. Europhys. Lett. 90, 45001 (2010).
  28. Darwin, C. The gravity field of a particle. Proc. R. Soc. Lond. 249, 180194 (1959).
  29. Su, F. S. & Mallett, R. L. The effect of the Kerr metric on the plane of polarization of an electromagnetic wave. Astrophys. J. 238, 11111125 (1980).
  30. Mendonça, J. T. & Thidé, B. Neutrino orbital angular momentum in a plasma vortex. Europhys. Lett. 84, 41001 (2008).

Download references

Author information

Affiliations

  1. Department of Astronomy, University of Padova, vicolo dell’Osservatorio 3, IT-35122 Padova, Italy

    • Fabrizio Tamburini
  2. Swedish Institute of Space Physics, Box 537, Ångström Laboratory, SE-75121 Uppsala, Sweden

    • Bo Thidé
  3. QsciTech and Department of Physics and Astronomy, Macquarie University, 2109 New South Wales, Australia

    • Gabriel Molina-Terriza
  4. ICFO, Parc Mediterrani de la Tecnologia, Av. del Canal Olı´mpic s/n, ES-08860 Castelldefels (Barcelona), Spain

    • Gabriele Anzolin

Contributions

F.T., B.T. and G.M-T. developed the model. F.T. carried out the numerical simulations. G.A. calculated and plotted the OAM spectra. F.T. and B.T. wrote the manuscript. All authors discussed and commented on the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary Information (800k)

    Supplementary Information

Additional data