Introduction

The purpose of this exercise is to get some hands-on experience with the numerical integration of ODE systems. We will integrate the geodesic equations in the Schwarzschild spacetime and those of a relativistic stellar model. There are some subtleties and potential pitfalls one should be aware of even when dealing with the numerics of relatively simple ODEs, but our main focus here is to illustrate some simple physics concepts. As the instructor has pointed out many times, The non-linearity of the most simple equations sometimes produce a rich phenomenology, as in the case of the TOV equations.