Numerical Solutions to McVittie Timelike Geodesics

Numerical solutions are provided to timelike geodesics within the Schwarzschild and McVittie metrics. The Schwarzschild metric represents a static, non-spinning black hole. The McVittie metric appears to be Schwarzschild close to the origin, but an expanding FLRW space (cosmology) far away. The main goal of this research is to show the difference in the orbital and gravitational wave patterns between static and expanding spacetimes. Both FLRW and Schwarzschild-DeSitter spacetimes are discussed within the numerical context of calculating geodesics. The numerical method used is an 8th order Runge-Kutta coded within Python.