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## Main Question or Discussion Point

I know that a black hole creates infinite curvature in spacetime and hence infinite time dilation. I was wondering though, if I could think of this stopping of time due to the fact that a light ray moving radially towards the centre of a black hole would have to travel infinitely far along the coordinate system's proper radial axis to reach the black hole's centre, as the infinite curvature would produce a proper radial distance tending to infinity as the light ray gets closer to the singularity?