In this work, we investigated whether the Pseudo-Newtonian theory (PNP) is applicable to black hole solution in modified gravity. In this regard, as an example, a static spherically symmetric 4D AdS Schwarzschild Yang-Mills black hole in EinsteinGauss-Bonnet gravity is considered. Also, a brief discussion on the structure and horizons of this black hole spacetime is presented. We calculated angular momentum and energy in the framework of the general theory of relativity as well as in PNP theory. In both of these framework, a graphical comparison of angular momentum has been studied

In this paper, we investigated the trajectory of the massive particle in the vicinity of a general spherical symmetric black hole. Also, in the framework of general sphericalily symmetric black hole, Pseudo-Newtonian potential (PNP) and effective potentials has been investigated. As an example, static spherically symmetric black hole in f(R) gravity is considered and presented the brief discussion on the structure of spacetime and horizons. We calculated energy and angular momentum in the framework of general relativity as well as in Pseudo-Newtonian theory. A graphical comparison of angular momentum in this both framework has been studied.

Study of perihelion shift of Mercury and deflection angle are important aspects for the verification of general relativity. For Schwarzschild geometry both the perihelion shift and weak deflection angle were independent of charge whereas for ReissnerNordstrom space-time charge should effect on both the perihelion shift and deflection angle. This paper shows the perihelion shift decreases with the increases of charge. Effect of other parameters like angular momentum, mass parameter, distance of closest approach on perihelion precession and deflection angle has also discussed. This paper also includes the graphical behavior which verifes our theoretical calculations.