Abstract
The paper aims to study the geometry and physics of the Raychaudhuri equation (RE) in the background of a homogeneous and anisotropic space–time described by Kantowski–Sachs (KS) metric. Role of anisotropy/shear in the context of convergence and possible avoidance of singularity has been analyzed subject to a physically motivated constraint. Moreover, using a suitable transformation the first order RE has been converted to a second order differential equation analogous to a Harmonic Oscillator and criterion for convergence has been shown to be associated with the time varying frequency of the Oscillator. Finally, the paper points out a geometric and physical notion of anisotropy along with their corresponding behavior towards convergence.
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