“Dynamics of particles around stellar black holes

Abstract

The Schwarzschild solution is unique and its metric can be interpreted as the exterior gravitational field of a spherically symmetric mass. Most of the experimental tests of general relativity were based on the Schwarzschild geometry in the region r > 2GM c 2 . Some are based on the trajectories of massive particles and others on photons trajectories.In this thesis we did study this issue theoretically. In our derivations,we considered the Einstein’s field equations and equations of motion for massive particle and photons where we did derive the relevant dynamical equations and observable parameters. Then, we did generate numerical solutions of effective potentials using MATHEMATICA. As a result ,Schwarzschild solution possesses stable circular orbits for r > 6GM c 2 and unstable circular orbits for 3GM c 2 < r < 6GM c 2 .