Simulated image of the shadow of the Kerr–Newman–NUT–Kiselev black hole in the Rastall gravity with a thin accretion disk
Department of Physics, Center for Field Theory and Particle Physics, Fudan University, 200438, Shanghai, China
2 National University of Uzbekistan, 100174, Tashkent, Uzbekistan
3 Shanghai Astronomical Observatory, 200030, Shanghai, China
4 School of Astronomy and Space Science, University of Chinese Academy of Sciences, 100049, Beijing, China
5 Ulugh Beg Astronomical Institute, Astronomy St. 33, 100052, Tashkent, Uzbekistan
6 Akfa University, Milliy Bog’ Street 264, 111221, Tashkent, Uzbekistan
7 Samarkand State University, University Avenue 15, 140104, Samarkand, Uzbekistan
8 Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Kori Niyoziy 39, 100000, Tashkent, Uzbekistan
9 School of Electrical Engineering and Computer Science, National University of Sciences and Technology, H-12, Islamabad, Pakistan
10 Institute of Nuclear Physics, Ulugbek 1, 100214, Tashkent, Uzbekistan
11 Tashkent State Technical University, 100095, Tashkent, Uzbekistan
Accepted: 26 December 2022
Published online: 19 January 2023
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 , for the quintessence, reduces the thermal flux for very small values of the Rastall parameter . 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 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 , when the parameter is close to zero and it becomes considerable when the parameter 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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