On the Raychaudhuri equation

GEORGE F R ELLIS

Mathematics Department, University of Cape Town, Rondebosch,

Cape Town, South Africa

E-mail: Ellis@MATHS.uct.ac.za

Abstract. The Raychaudhuri equation is central to the understanding

of gravitational attraction in astrophysics and cosmology, and in

particular underlies the famous singularity theorems of general

relativity theory. This paper reviews the derivation of the equation,

and its significance in cosmology.

Keywords. General relativity; singularity; cosmology.

PACS Nos 04.20.Dw; 47.75.+f; 95.30.Sf; 98.80.-k; 98.80.Jk