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A plot showing radial geodesics of the Schwarzschild black hole, in Eddington-Finkelstein coordinates that are well-suited to describing the entire spacetime outside the singularity. The ingoing geodesics v = constant are shown as blue lines. The geodesics 2 dr - V(r) dv = 0 are shown as red curves. Outside r = 2MG they are outgoing, inside r=2MG they are ingoing. Looking at the intersection of these blue and red curves, you can see how the light cones at a point tilt as one approaches r = 2MG. Inside this region the light cones are tilted so that the causal paths followed by any observer lead inexorably inward.