Abstract
We present firstly the equation of motion for the photon coupled to a special bumblebee vector field in a Kerr black hole spacetime and find that the propagation of light depends on its polarization due to the birefringence phenomenon. The dependence of black hole shadow on the light's polarization is dominated by the rotation of black hole. In the non-rotating case, we find that the black hole shadow is independent of the polarization of light. However, the status is changed in the rotating case, in which the black hole shadow depends on the light's polarization and the coupling between bumblebee vector field and electromagnetic field. These features of black hole shadow casted by polarized lights could help us to understand the bumblebee vector field with Lorentz symmetry breaking and its interaction with electromagnetic field.
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References
Event Horizon Telescope collaboration, First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, Astrophys. J. 875 (2019) L1 [arXiv:1906.11238] [INSPIRE].
Event Horizon Telescope collaboration, First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole, Astrophys. J. Lett. 875 (2019) L6 [arXiv:1906.11243] [INSPIRE].
S. Vagnozzi and L. Visinelli, Hunting for extra dimensions in the shadow of M87*, Phys. Rev. D 100 (2019) 024020 [arXiv:1905.12421] [INSPIRE].
I. Banerjee, S. Chakraborty and S. SenGupta, Silhouette of M87*: A new window to peek into the world of hidden dimensions, Phys. Rev. D 101 (2020) 041301 [arXiv:1909.09385] [INSPIRE].
Y. Chen, J. Shu, X. Xue, Q. Yuan and Y. Zhao, Probing Axions with Event Horizon Telescope Polarimetric Measurements, Phys. Rev. Lett. 124 (2020) 061102 [arXiv:1905.02213] [INSPIRE].
R.A. Konoplya, Shadow of a black hole surrounded by dark matter, Phys. Lett. B 795 (2019) 1 [arXiv:1905.00064] [INSPIRE].
X. Hou, Z. Xu, M. Zhou and J. Wang, Black Hole Shadow of Sgr A* in Dark Matter Halo, JCAP 07 (2018) 015 [arXiv:1804.08110] [INSPIRE].
K. Jusufi, M. Jamil, P. Salucci, T. Zhu and S. Haroon, Black Hole Surrounded by a Dark Matter Halo in the M87 Galactic Center and its Identification with Shadow Images, Phys. Rev. D 100 (2019) 044012 [arXiv:1905.11803] [INSPIRE].
P.V.P. Cunha, C.A.R. Herdeiro and E. Radu, EHT constraint on the ultralight scalar hair of the M87 supermassive black hole, Universe 5 (2019) 220 [arXiv:1909.08039] [INSPIRE].
C. Li et al., Testing the equivalence principle via the shadow of black holes, Phys. Rev. Res. 2 (2020) 023164 [arXiv:1912.12629] [INSPIRE].
Y. Huang, S. Chen and J. Jing, Double shadow of a regular phantom black hole as photons couple to the Weyl tensor, Eur. Phys. J. C 76 (2016) 594 [arXiv:1606.04634] [INSPIRE].
G.T. Zatsepin and V.A. Kuzmin, Upper limit of the spectrum of cosmic rays, JETP Lett. 4 (1966) 78 [INSPIRE].
M. Takeda et al., Extension of the cosmic ray energy spectrum beyond the predicted Greisen-Zatsepin-Kuz’min cutoff, Phys. Rev. Lett. 81 (1998) 1163 [astro-ph/9807193] [INSPIRE].
R. Casana, A. Cavalcante, F.P. Poulis and E.B. Santos, Exact Schwarzschild-like solution in a bumblebee gravity model, Phys. Rev. D 97 (2018) 104001 [arXiv:1711.02273] [INSPIRE].
V. Kostelecky and S. Samuel, Gravitational Phenomenology in Higher Dimensional Theories and Strings, Phys. Rev. D 40 (1989) 1886 [INSPIRE].
O. Bertolami and J. Paramos, The Flight of the bumblebee: Vacuum solutions of a gravity model with vector-induced spontaneous Lorentz symmetry breaking, Phys. Rev. D 72 (2005) 044001 [hep-th/0504215] [INSPIRE].
Q.G. Bailey and V. Kostelecky, Signals for Lorentz violation in post-Newtonian gravity, Phys. Rev. D 74 (2006) 045001 [gr-qc/0603030] [INSPIRE].
R. Bluhm, N.L. Gagne, R. Potting and A. Vrublevskis, Constraints and Stability in Vector Theories with Spontaneous Lorentz Violation, Phys. Rev. D 77 (2008) 125007 [Erratum ibid. 79 (2009) 029902] [arXiv:0802.4071] [INSPIRE].
V. Kostelecky and J. Tasson, Prospects for Large Relativity Violations in Matter-Gravity Couplings, Phys. Rev. Lett. 102 (2009) 010402 [arXiv:0810.1459] [INSPIRE].
M.D. Seifert, Generalized bumblebee models and Lorentz-violating electrodynamics, Phys. Rev. D 81 (2010) 065010 [arXiv:0909.3118] [INSPIRE].
R.V. Maluf, C.A.S. Almeida, R. Casana and M. Ferreira, Einstein-Hilbert graviton modes modified by the Lorentz-violating bumblebee Field, Phys. Rev. D 90 (2014) 025007 [arXiv:1402.3554] [INSPIRE].
J. Páramos and G. Guiomar, Astrophysical Constraints on the Bumblebee Model, Phys. Rev. D 90 (2014) 082002 [arXiv:1409.2022] [INSPIRE].
C.A. Escobar and A. Martín-Ruiz, Equivalence between bumblebee models and electrodynamics in a nonlinear gauge, Phys. Rev. D 95 (2017) 095006 [arXiv:1703.01171] [INSPIRE].
J.F. Assunção, T. Mariz, J.R. Nascimento and A.Y. Petrov, Dynamical Lorentz symmetry breaking in a tensor bumblebee model, Phys. Rev. D 100 (2019) 085009 [arXiv:1902.10592] [INSPIRE].
A. Ovgun, K. Jusufi and I. Sakalli, Gravitational Lensing Under the Effect of Weyl and Bumblebee Gravities: Applications of Gauss-Bonnet Theorem, Annals Phys. 399 (2018) 193 [arXiv:1805.09431] [INSPIRE].
S. Kanzi and I. Sakalli, G UP Modified Hawking Radiation in Bumblebee Gravity, Nucl. Phys. B 946 (2019) 114703 [arXiv:1905.00477] [INSPIRE].
C. Ding, C. Liu, R. Casana and A. Cavalcante, Exact Kerr-like solution and its shadow in a gravity model with spontaneous Lorentz symmetry breaking, Eur. Phys. J. C 80 (2020) 178 [arXiv:1910.02674] [INSPIRE].
C. Liu, C. Ding and J. Jing, Thin accretion disk around a rotating Kerr-like black hole in Einstein-bumblebee gravity model, arXiv:1910.13259 [INSPIRE].
Z. Li and A. Övgün, Finite-distance gravitational deflection of massive particles by a Kerr-like black hole in the bumblebee gravity model, Phys. Rev. D 101 (2020) 024040 [arXiv:2001.02074] [INSPIRE].
A. Övgün, K. Jusufi and I. Sakallı, Exact traversable wormhole solution in bumblebee gravity, Phys. Rev. D 99 (2019) 024042 [arXiv:1804.09911] [INSPIRE].
D. Capelo and J. Páramos, Cosmological implications of Bumblebee vector models, Phys. Rev. D 91 (2015) 104007 [arXiv:1501.07685] [INSPIRE].
T. Fujita, R Tazaki and K. Toma, Hunting Axion Dark Matter with Protoplanetary Disk Polarimetry, Phys. Rev. Lett. 122 (2019) 191101 [arXiv:1811.03525] [INSPIRE].
A.D. Plascencia and A. Urbano, Black hole superradiance and polarization-dependent bending of light, JCAP 04 (2018) 059 [arXiv:1711.08298] [INSPIRE].
I.T. Drummond and S.J. Hathrell, QED Vacuum Polarization in a Background Gravitational Field and Its Effect on the Velocity of Photons, Phys. Rev. D 22 (1980) 343 [INSPIRE].
R.D. Daniels and G.M. Shore, ‘Faster than light’ photons and charged black holes, Nucl. Phys. B 425 (1994) 634 [hep-th/9310114] [INSPIRE].
R.D. Daniels and G.M. Shore, ‘Faster than light’ photons and rotating black holes, Phys. Lett. B 367 (1996) 75 [gr-qc/9508048] [INSPIRE].
R-G. Cai, Propagation of vacuum polarized photons in topological black hole space-times, Nucl. Phys. B 524 (1998) 639 [gr-qc/9801098] [INSPIRE].
H.T. Cho, ‘Faster than light’ photons in dilaton black hole space-times, Phys. Rev. D 56 (1997) 6416 [gr-qc/9704014] [INSPIRE].
V.A. De Lorenci, R. Klippert, M. Novello and J.M. Salim, Light propagation in nonlinear electrodynamics, Phys. Lett. B 482 (2000) 134 [gr-qc/0005049] [INSPIRE].
D.A.R. Dalvit, F.D. Mazzitelli and C. Molina-Paris, One loop graviton corrections to Maxwell’s equations, Phys. Rev. D 63 (2001) 084023 [hep-th/0010229] [INSPIRE].
N. Ahmadi and M. Nouri-Zonoz, Quantum gravitational optics: The Induced phase, Class. Quant. Grav. 25 (2008) 135008 [gr-qc/0703123] [INSPIRE].
N. Breton, Geodesic structure of the Born-Infeld black hole, Class. Quant. Grav. 19 (2002) 601 [INSPIRE].
P.V.P. Cunha, C.A.R. Herdeiro, E. Radu and H.F. Runarsson, Shadows of Kerr black holes with scalar hair, Phys. Rev. Lett. 115 (2015) 211102 [arXiv:1509.00021] [INSPIRE].
P.V.P. Cunha, C.A.R. Herdeiro, E. Radu and H.F. Runarsson, Shadows of Kerr black holes with and without scalar hair, Int. J. Mod. Phys. D 25 (2016) 1641021 [arXiv:1605.08293] [INSPIRE].
F.H. Vincent, E. Gourgoulhon, C. Herdeiro and E. Radu, Astrophysical imaging of Kerr black holes with scalar hair, Phys. Rev. D 94 (2016) 084045 [arXiv:1606.04246] [INSPIRE].
P.V.P. Cunha, J. Grover, C. Herdeiro, E. Radu, H. Runarsson and A. Wittig, Chaotic lensing around boson stars and Kerr black holes with scalar hair, Phys. Rev. D 94 (2016) 104023 [arXiv:1609.01340] [INSPIRE].
J. Shipley and S.R. Dolan, Binary black hole shadows, chaotic scattering and the Cantor set, Class. Quant. Grav. 33 (2016) 175001 [arXiv:1603.04469] [INSPIRE].
A. Bohn et al., What does a binary black hole merger look like?, Class. Quant. Grav. 32 (2015) 065002 [arXiv:1410.7775] [INSPIRE].
M. Wang, S. Chen and J. Jing, Shadows of Bonnor black dihole by chaotic lensing, Phys. Rev. D 97 (2018) 064029 [arXiv:1710.07172] [INSPIRE].
J. Grover and A. Wittig, Black Hole Shadows and Invariant Phase Space Structures, Phys. Rev. D 96 (2017) 024045 [arXiv:1705.07061] [INSPIRE].
T. Johannsen, Photon Rings around Kerr and Kerr-like Black Holes, Astrophys. J. 777 (2013) 170 [arXiv:1501.02814] [INSPIRE].
R. Roy and U. Yajnik, Evolution of black hole shadow in the presence of ultralight bosons, Phys. Lett. B 803 (2020) 135284 [arXiv:1906.03190] [INSPIRE].
Z. Younsi, A. Zhidenko, L. Rezzolla, R. Konoplya and Y. Mizuno, New method for shadow calculations: Application to parametrized axisymmetric black holes, Phys. Rev. D 94 (2016) 084025 [arXiv:1607.05767] [INSPIRE].
M. Wang, S. Chen and J. Jing, Chaotic shadow of a non-Kerr rotating compact object with quadrupole mass moment, Phys. Rev. D 98 (2018) 104040 [arXiv:1801.02118] [INSPIRE].
S.-W. Wei and Y.-X. Liu, Testing the nature of Gauss-Bonnet gravity by four-dimensional rotating black hole shadow, arXiv:2003.07769 [INSPIRE].
V. Frolov and I. Novikov, Black Hole Physics: Basic concepts and new developments, Kluwer Academic Publishers, Berlin Germany (1998).
K. Hioki and K.-i. Maeda, Measurement of the Kerr Spin Parameter by Observation of a Compact Object’s Shadow, Phys. Rev. D 80 (2009) 024042 [arXiv:0904.3575] [INSPIRE].
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Chen, S., Wang, M. & Jing, J. Polarization effects in Kerr black hole shadow due to the coupling between photon and bumblebee field. J. High Energ. Phys. 2020, 54 (2020). https://doi.org/10.1007/JHEP07(2020)054
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DOI: https://doi.org/10.1007/JHEP07(2020)054