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Simulated image of the shadow of the Kerr–Newman–NUT–Kiselev black hole in the Rastall gravity with a thin accretion disk

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Abstract

Here, we study the effect of strong gravitational field on the light rays emitted from the particles in the accretion disk in the vicinity of the Kerr–Newman–NUT–Kiselev (KNNK) black hole in the Rastall gravity (RG). In our analysis we consider the thin accretion disk model of Novikov and Thorne. We observe that the thermal flux of the accretion disk strongly depends on the intensity of the quintessence in the spacetime of the KNNK black hole in the RG, and the flux decreases for the increasing values of the quintessential intensity. We also notice that the smaller values of the equation of state parameter \(\omega _q\), for the quintessence, reduces the thermal flux for very small values of the Rastall parameter \(\kappa \lambda \). Further we use the numerical codes, namely, the GYOTO and TM (Temurbek Mirzaev) codes, using C++ and Python languages, to compare the shadow cast by the KNNK black hole in the RG. We see that both the codes give similar behavior of the shadow cast by the KNNK black hole in the RG. Interestingly, we observe that the left hand side of the apparent black hole environment with respect to the central black hole is much brighter than the right hand side. This is due to the Doppler effect, i.e. the frequency of photons coming towards the observer (and thus the observed flux energy) is always higher than those of moving away form the observer. We demonstrate that increase of the quintessential intensity increases the size of the shadow cast by the KNNK black hole in the RG, considerably when the parameter \(\kappa \lambda \) is very close to zero. We also see that the change in the size of the shadow of the KNNK black hole in the RG becomes negligible with the change in the quintessential intensity parameter \(\alpha \), when the parameter \(\omega _q\) is close to zero and it becomes considerable when the parameter \(\omega _q\) is smaller than zero. Next, we show that the position and shape of the shadow cast by the KNNK black hole in the RG strongly depends on the inclination angle of the incident light. We notice that the shadow of the KNNK black hole in the RG has more circular-like form for smaller values of the inclination angle. Further the shadow of the KNNK black hole in the RG shifts towards the right and becomes more deformed with the increasing values of the inclination angle.

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Data Availability Statement

This manuscript has no associated data, or the data will not be deposited. (There are no observational data related to this article. The necessary calculations and graphic discussion can be made available on request).

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Acknowledgements

This research is supported by Grants F-FA-2021-432, F-FA-2021-510 and MRB-2021-527 of the Uzbekistan Ministry for Innovative Development. A.A. and B.A. acknowledge the support of Uzbekistan Ministry for Innovative Development Grants and the Abdus Salam International Centre for Theoretical Physics under the Grant No. OEA-NT-01.

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Authors and Affiliations

  1. Department of Physics, Center for Field Theory and Particle Physics, Fudan University, Shanghai, 200438, China

    Temurbek Mirzaev

  2. National University of Uzbekistan, Tashkent, 100174, Uzbekistan

    Temurbek Mirzaev, Ahmadjon Abdujabbarov & Bobomurat Ahmedov

  3. Shanghai Astronomical Observatory, Shanghai, 200030, China

    Song Li

  4. School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing, 100049, China

    Song Li & Bobomurat Ahmedov

  5. Ulugh Beg Astronomical Institute, Astronomy St. 33, Tashkent, 100052, Uzbekistan

    Bakhtiyor Narzilloev & Ahmadjon Abdujabbarov

  6. Akfa University, Milliy Bog’ Street 264, Tashkent, 111221, Uzbekistan

    Bakhtiyor Narzilloev

  7. Samarkand State University, University Avenue 15, Samarkand, 140104, Uzbekistan

    Bakhtiyor Narzilloev

  8. Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Kori Niyoziy 39, Tashkent, 100000, Uzbekistan

    Bakhtiyor Narzilloev, Ahmadjon Abdujabbarov & Bobomurat Ahmedov

  9. School of Electrical Engineering and Computer Science, National University of Sciences and Technology, H-12, Islamabad, Pakistan

    Ibrar Hussain

  10. Institute of Nuclear Physics, Ulugbek 1, Tashkent, 100214, Uzbekistan

    Ahmadjon Abdujabbarov

  11. Tashkent State Technical University, Tashkent, 100095, Uzbekistan

    Ahmadjon Abdujabbarov

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  1. Temurbek Mirzaev
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  2. Song Li
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Correspondence to Ibrar Hussain.

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Mirzaev, T., Li, S., Narzilloev, B. et al. Simulated image of the shadow of the Kerr–Newman–NUT–Kiselev black hole in the Rastall gravity with a thin accretion disk. Eur. Phys. J. Plus 138, 47 (2023). https://doi.org/10.1140/epjp/s13360-022-03632-4

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