Consider the metric corresponding to the Schwarzchild solution. It represents a Non-rotating Black hole. When we want to understand the causal structure of the spacetime we find the null geodesic equation.
Outgoing radial null geodesic - The outgoing null geodesics are drawn in region r>2m and r<2m. For r>2m, the null geodesics go to infinity as we expect. For r<2m, it goes and hits the singularity. But these are outgoing null geodesics in the region r<2m seems to be coming from the horizon at time t=-(infinity). Are these outgoing null geodesics in both the regions somehow connected at t=-(infinity)?
Ingoing radial null geodesic- The ingoing null geodesics are drawn similarly in region r<2m and r>2m. In the region r<2m, the geodesics come from the horizon and hits the singularity. They start at t=+(infinity) and hits the singularity at some finite time which is less that infinity. Do these null geodesics travel back in time in this region?