Geodesic congruences in modified Schwarzschild black holes

We investigate two different kinds of modified Schwarzschild black holes: A regularized Schwarzschild black hole and a quantum deformed Schwarzschild black hole. We study the geodesics and geodesic congruences in these two modified Schwarzschild black holes. In particular, we calculate the expansion of radial timelike and null geodesic congruences. Based on these results, we discuss some similarities and differences between these two kinds of modified Schwarzschild black holes