# Johan Michel Chavez Tovar

## Higher order curvature terms corrections in the Raychaudhuri equation

In general relativity, gravity is attractive. This feature is present in the Raychaudhuri equation provided the strong or weak energy conditions are fulfilled. In this scenario the expansion of a congruence of geodesics is consistently decreasing. As it is well known Raychaudhuri equation is an important component of singularity theorem which shows that spacetime is geodesically incomplete implying that general relativity is itself incomplete. It is possible that modified versions of general relativity in particular the inclusion of higher order curvature terms can resolve or attenuate this kind of singularities. It is important then to study the behavior of geodesic congruences in these theories.

In this work, we present a brief review of the Raychaudhuri equation, we begin with a summary of the essential features of this equation, and we move on to a discussion of the equation in the context of the alternative gravitation theory known as Critical Gravity. Finally, we discuss some effects of Critical Gravity theory in the Raychaudhuri equation and the geodesic congruences in an AdS type black hole solution.