Raychaudhuri equetion

The Raychaudhuri equation is sometimes referred to as the Landau–Raychaudhuri equation. It may be worthwhile to point out precisely, the work of Landau, in relation to this equation. Landau’s contribution appears in his treatise The Classical Theory of Fields [10] and is also discussed in detail in [6,11]. ... where γ is the determinant of the 3-metric ... While deriving the inequality, Landau implicitly assumes the strong energy condition (though it is not mentioned with this name). Then, using it, he is able to show that γ must necessarily go to zero within a finite time. However, he mentions quite clearly that this does not imply the existence of a physical singularity in the sense of curvature. Though Landau’s work captures the essence of focusing, he does not explicitly mention geodesic focusing. Moreover, he does not introduce shear and rotation or write down the complete equation for the expansion.