Wave Optics in the Kerr Space-Time Taking the Spin-Helicity Interaction into Account
Keywords:one-way null field, Maxwell spinor, the Kerr space-time, separation of variables, wave vector, geodesics
We apply an algebraically special solution of the Maxwell equations in the Kerr space-time, which we specify as outgoing in the Chandrasekhar meaning, to obtain the wave vectors of right- and left-polarized waves and prove that the nullity condition of field invariants yield the non-nullity of wave vectors and that the wave vector is not geodesic. We also show how these are related to the analysis of radiation in the Kerr space-time, provided by Starobinskii and Teukolsky.
B.P. Abbott et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 6 (2016). https://gcn.gsfc.nasa.gov/gcn3/25333.gcn3.
K. Akiyama et al. First M87 event horizon telescope results. I. The shadow of the supermassive black hole. Astrophys. J. 875, (2019).
R. Konoplya, L. Rezzolla, A. Zhidenko. General parametrization of axisymmetric black holes in metric theories of gravity. Phys. Rev. D 93, 064015 (2016). https://doi.org/10.1103/PhysRevD.93.064015
J. Abedi, H. Dykaar, N. Afshordi. Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons. Phys. Rev. D 96, 082004 (2017). https://doi.org/10.1103/PhysRevD.96.082004
A. Mitra, C. Corda, H.J. Mosquera Cuesta. How to distinguish an actual astrophysical magnetized black hole mimicker from a true (theoretical) black hole. http://arxiv.org/abs/1908.06815v1.
A. Starobinskii. Amplification of waves during reflection from a rotating "black hole". Zh. Eksp. Teor. Fiz. 64, 48 (1973).
W.H. Press, S.A. Teukolsky. Floating orbits, superradiant scattering and the black-hole bomb. Nature 238, 211 (1972). https://doi.org/10.1038/238211a0
S. Teukolsky. Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations. The Astrophysical Journal 185, 635 (1973). https://doi.org/10.1086/152444
A. Starobinsky, S. Churilov. Amplification of electromagnetic and gravitational waves scattered by a rotating black hole. Sov. Phys. - JETP 38, 1 (1974).
S. Teukolsky. The Kerr metric. Astrophys. J. 32, 124006 (2015). https://doi.org/10.1088/0264-9381/32/12/124006
M. Casals, A. C. Ottewill, N. Warburton. High-order asymptotics for the spin-weighted spheroidal equation at large real frequency. arXiv:1810.00432v1 [gr-qc].
B. Mashhoon. Scattering of electromagnetic radiation from a black hole. Phys. Rev. D 7, 2807 (1973). https://doi.org/10.1103/PhysRevD.7.2807
V. Pelykh, Y. Taistra. A class of general solutions of the Maxwell equations in the Kerr space-time. J. Math. Sci. 229, No. 2, 162 (2018). https://doi.org/10.1007/s10958-018-3668-5
V. Pelykh, Y. Taistra. Solution with separable variables for null one-way Maxwell field in Kerr space-time. Acta Phys. Polon. Supp. 10, 387 (2017). https://doi.org/10.5506/APhysPolBSupp.10.387
V. Pelykh, Y. Taistra. Null one-way fields in the Kerr spacetime. Ukr. J. Phys. 62, No. 11, 1007 (2017). https://doi.org/10.15407/ujpe62.11.1007
V. Pelykh, Y. Taistra. On the null one-way solution to Maxwell equations in the Kerr space-time. Math. Model. Comput. 5, No. 2, 201 (2018). https://doi.org/10.23939/mmc2018.02.201
E. Guadagnini. Gravitational deflection of light and helicity asymmetry. Phys. Lett. B 548, Iss. 1-2, 19 (2002). https://doi.org/10.1016/S0370-2693(02)02811-3
A. Barbieri, E. Guadagnini. Gravitational optical activity. Nucl. Phys. 703, Iss. 1, 391 (2004). https://doi.org/10.1016/j.nuclphysb.2004.10.025
V. Frolov, A. Shoom. Scattering of circularly polarized light by a rotating black hole. Phys. Rev. D 86, Iss. 2, 024010 (2012). https://doi.org/10.1103/PhysRevD.86.024010
F. Asenjo, S. Hojman. Do electromagnetic waves always propagate along null geodesics? Class. and Quant. Gravity 34, No. 20, 205011 (2017). https://doi.org/10.1088/1361-6382/aa8b48
S. Chandrasekhar. On algebraically special perturbations of black holes. Proc. R. Soc. London, Ser. A 392, 1 (1984). https://doi.org/10.1098/rspa.1984.0021
R. Plyatsko. Manifestations of Gravitational Ultrarelativistic Spin-Orbit Interaction (Naukova Dumka, 1988) (in Ukrainian).
R. Plyatsko, M. Fenyk. Highly relativistic circular orbits of spinning particle in the Kerr field. Phys. Rev. D 87, No. 4, 044019 (2013). https://doi.org/10.1103/PhysRevD.87.044019
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