Geodesic RHS uses the Schwarzschild metric and the geodesic equation to calculate:

d1 = current speed of movement
d2 = change in that speed (from gravity)

So essentially, we calculate how gravity turns the light around the black hole in terms of the radius, theta, and phi components.

Runge-Kutta 4 is a more precise way to step forward in a simulation. Basically we take 4 smaller steps to sample derivatives across the interval, and based on that knowledge we calculate the most accurate path forward.