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We investigate analytically the apparent shadows cast by Kerr-Newman black hole with surrounding perfect fluid matter in Rastall gravity theory. With the help of the Hamilton-Jacobi equation and Carter constant separable method, we derive the null geodesics of the black hole space-time and calculate the numerical results of the horizon structures. The results reveal that three horizons (Cauchy horizon r-, event horizon r+ and cosmological horizon rq) occur in the space-time, and the horizon structure could degenerate while the Rastall parameter kλ arrives the critical value. By fixing the value of equation state parameter ∼ω of surrounding substance for both cases of dark matter (∼ω = -1⁄3) and dark energy (∼ω = -2⁄3), we study the effects of the perfect fluid matter intensity Ns, the Rastall parameter kλ, the black hole spin a and the black hole charge Q on black hole shadows in detail. Furthermore, the effective potentials for black hole space-time and the energy emission rate of the black hole are also conducted and discussed.
We investigate analytically the apparent shadows cast by Kerr-Newman black hole with surrounding perfect fluid matter in Rastall gravity theory. With the help of the Hamilton-Jacobi equation and Carter constant separable method, we derive the null geodesics of the black hole space-time and calculate the numerical results of the horizon structures. The results reveal that three horizons (Cauchy horizon r-, event horizon r+ and cosmological horizon rq) occur in the space-time, and the horizon structure could degenerate while the Rastall parameter kλ arrives the critical value. By fixing the value of equation state parameter ∼ω of surrounding substance for both cases of dark matter (∼ω = -1⁄3) and dark energy (∼ω = -2⁄3), we study the effects of the perfect fluid matter intensity Ns, the Rastall parameter kλ, the black hole spin a and the black hole charge Q on black hole shadows in detail. Furthermore, the effective potentials for black hole space-time and the energy emission rate of the black hole are also conducted and discussed.
We present the horizon structures and the shadows for Kerr-Newman-AdS black hole located in perfect fluid matter field in Rastall gravity. By considering the Hamilton-Jacobi equation and Carter constant separable method, we obtain the null geodesic equations of the black hole space-time as well as the unstable circular photon orbits in terms of the impact parameters. The horizon structures of the space-time are calculated numerically. The results show that there are four roots for a general case of the horizon equation (the Cauchy horizon r − h , the event horizon r + h , the cosmological horizon r q of Rastall gravity and the cosmological horizon r c of cosmological constant), which lead to a specific characteristic with the subregions of the space-time. The influences of the cosmological horizons r q and r c on the light trajectories around the black hole are also investigated. Furthermore, we study the effects of the parameters, including the perfect fluid matter intensity N s , the Rastall parameter k λ, the cosmological constant Λ, the black hole spin a and the black hole charge Q on black hole shadows in detail.
In this study, we focus on a black hole immersed in a cosmological Chaplygin-like dark fluid (CDF), characterized by the equation of state p = -B/ρ and an additional parameter q influencing the energy density of the fluid. We investigate the geodesic structure, shadow, and optical appearance of such a black hole. Through analysis on the effective potential and the epicyclic frequencies, it is found that the existence of innermost/outermost stable circular orbits for a timelike particle is governed by the CDF parameters. The behaviors of the orbital conserved quantities and Keplerian frequency are also examined. Due to the existence of pseudo-cosmological horizon, the determination of the shadow radius depends significantly on the position of the observer. By placing the static observer at an approximately flat position between the event and pseudo-cosmological horizons, we constrain the CDF parameters using EHT observations. We investigate the effect of CDF on the shadows and optical images of the black hole, surrounded by various profiles of accretions. For the thin disk accretion, the light trajectories are categorized into direct emission, lensing ring, and photon ring based on impact parameters. Due to the existence of outermost stable circular orbits, outer edges could exist in the direct and lensing ring images. The observed brightness is mainly due to direct emission, with a minor contribution from the lensing ring, while the contribution from the photon ring is negligible due to extreme demagnetization. In the case of spherical accretion, we consider both static and infalling accretion models. The images obtained under infalling accretion are slightly darker than those under static accretion, attributed to the Doppler effect. Throughout the study, we analyze the influence of the parameters B and q on the results.
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