Higher-Order Curvature Corrections in the Raychaudhuri Equation

Within the framework of general relativity, gravity is characterized as attractive. This characteristic is evident in the Raychaudhuri equation when the strong or weak energy conditions are satisfied. Under these conditions, the expansion of a congruence of geodesics consistently decreases. It is widely acknowledged that the Raychaudhuri equation plays a primordial role in singularity theorems, revealing that spacetime is geodesically incomplete and suggesting an inherent incompleteness in general relativity itself. There is a possibility that modified versions of general relativity, especially those incorporating higher-order curvature terms, could potentially resolve or alleviate such singularities.