Our simple little lives here on earth: Use euklian geomety: ds**2 = dx**2 + dy**2
Theory of relativity:
Spesial: only applies when aceleration = 0. Can use lorentz geometry. ds**2 = dt**2 – (dx**2 + dy**2 + dz**2)
General: applies anywhere. Use schwartschild geometry. ds**2 = (1-2m/r)dt**2 – dr**2/(1-2m/r) – r**2*dø**2
End of time: when r = 0 i guess. witch is the case in the center of a black hole. Or maybe the end of the value of time, more accurately..

dø = angle between events
m = mass [measured in meters]
r = distance from a poit to an event [meters]
dr = distance between two  events [meters]
dt = time distance between two events [meters]
ds = spacetime interval. Is the same for all observers!