Singularity in the Expansion of Geodesic congruences

My question is regarding the following graph,

The $X$-axis is the $r$ coordinate of the $(t,r,theta,phi)$ system, and the $Y$-axis is the expansion $Theta$ of a congruence of weakly bound, timelike, radial geodesics. There is only a physical (curvature) singularity at $O$. However after some calculations, I obtained the graph above, where $Theta$ is seen to diverge at a finite value. This is specifically for outgoing geodesics (invert the graph for ingoing geodesics)

Question:
What is the interpretation of this scenario just from the graph above?

My guess is that, outgoing radial geodesics all converge at the value $r = r_P$ (for the weakly bound condition) and can never go out to infinity. If this reasoning is correct, does this mean that a cloud of dust following such a congruence abruptly ends/stops at the boundary denoted by $r_p$ or a caustic is formed there, or is the behaviour of the dust something else?