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Shadow cast by Kerr-like black hole in the presence of plasma in Einstein-bumblebee gravity

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Abstract

In the Einstein-bumblebee gravity, the Lorentz symmetry is spontaneously broken by a vector field. In this paper, we attempt to test the Lorentz symmetry via the observation of the shadow cast by the Kerr-like black hole with or without plasma. A novel phenomenon of the Lorentz-violating parameter on the shadow is observed. The result shows that when the observer gradually moves from the poles to the equatorial plane, the shadow radius \(R_\mathrm{s}\) firstly decreases and then increases with the Lorentz-violating parameter. Such nonmonotonic behavior provides us an important understanding on the black hole shadow in the Einstein-bumblebee gravity. Besides, three more distortion observables are calculated, and found to increase with the Lorentz-violating parameter. The influence of the Lorentz-violating parameter on the deflection angle of light rays is also calculated via the Gauss-Bonnet theorem. When a homogeneous plasma is present, the motion of the photon is analyzed. We further observe that the frequency of plasma shrinks the size, while enhances the deformation of the shadow. Finally, adopting the observed data of the diameter of M87\(^*\), we find the favored range of some parameters.

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Acknowledgements

We thank Dr. Zi-Chao Lin for helpful discussions. This work was supported by the National Natural Science Foundation of China (Grants No. 12075103 and No. 11675064), the 111 Project (Grant No. B20063), and the Fundamental Research Funds for the Central Universities (No. Lzujbky-2019-ct06).

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  1. Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, School of Physical Science and Technology, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Hui-Min Wang & Shao-Wen Wei

  2. Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Hui-Min Wang & Shao-Wen Wei

  3. Academy of Plateau Science and Sustainability, Qinghai Normal University, Xining, 810016, People’s Republic of China

    Hui-Min Wang & Shao-Wen Wei

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Wang, HM., Wei, SW. Shadow cast by Kerr-like black hole in the presence of plasma in Einstein-bumblebee gravity. Eur. Phys. J. Plus 137, 571 (2022). https://doi.org/10.1140/epjp/s13360-022-02785-6

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