Null Geodesics, Raychaudhuri Equation, Trapped Surfaces, and Penrose Singularity Theorem

Abstract

We review the concept of congruence of null geodesics, the Raychaudhuri equation for the expansion, its harmonic oscillator version and associated "quantum" propagator, the role of the equation in the derivation of the Penrose singularity theorem, the definition of trapped surfaces, and the derivation of the theorem itself.