My question is regarding how spacetime looks like beyond the event horizon of a black hole, in particular how distances behave. In the Minkowski diagram of a black hole, all paths leads to the singularity. But what is the magnitude of the distances involved here? Let's say a neutron star is slowly accumulating mass, and eventually the Schwarzschild radius overtakes the radius of the star, causing it to collapse into a black hole. Now all forces are overtaken by the curvature of spacetime, and all matter converges towards the singularity. But what distance (in the Minkowski metric) does matter on the boundary of the star have to travel to get there? Does it ever arrive? I'm sort of imagining an endless well (looking like the graph of y = -1/x^2) down which matter is traveling, slowly getting closer to the singularity, but still infinitely far away. What does the math say about this?