Aspects of Einstein's general relativity: A classical deformation of Schwarzschild spacetime

In this work, we explore the Schwarzschild geometry in a spherically symmetric gravitational field. We build the non-commutative equations of motion with the aid of the Hamiltonian function and modified algebra. We then study the implications of the non-commutative geometry on the trajectory of a light ray, traveling in null and particles geodesics. Also, we interpret the effect of non-commutativity in both the bending of light and the perihelion advance of Mercury. Therefore, introducing a non-commutative parameter provides a slight correction to the results of general relativity.