Space-time structures, light trajectories and shadows for Kerr-Newman-AdS black hole with surrounding perfect fluid matter in Rastall gravity

Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> , the event horizon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> , 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.