General Relativistic Effects and Elliptic Functions PDF

This collection of articles highlights all possible trajectories of particles and light under the influence of a gravitational field of all possible strengths that may exist in our universe, including that of a black hole; and it also highlights the beautiful mathematical formulas that can express all these trajectories, according to Einstein's theory of general relativity.

For this to be possible, the authors use mathematical functions called elliptic functions that can describe orbits, including the familiar circular, elliptical, parabolic and hyperbolic orbits.

Some readers can put aside technical terms such as "Schwarzschild metric" which simply specifies a certain condition that excludes cases such as a spinning black hole, and "Parameter Space" which simply specifies all possible energy, momentum of an object or light and the character of the massive body (black hole included), and go directly to see the mathematical expressions that describe the trajectories, and the relevant graphs.