The Raychaudhuri equations: A brief review

SAYAN KAR¹ and SOUMITRA SENGUPTA²

¹Department of Physics and Centre for Theoretical Studies,

Indian Institute of Technology, Kharagpur 721 302, India

²Department of Theoretical Physics, Indian Association for the Cultivation of Science,

Jadavpur, Kolkata 700 032, India

E-mail: sayan@phy.iitkgp.ernet.in; sayan@cts.iitkgp.ernet.in;

tpssg@mahendra.iacs.res.in

Abstract. We present a brief review on the Raychaudhuri equations. Beginning

with a summary of the essential features of the original article

by Raychaudhuri and subsequent work of numerous authors, we move

on to a discussion of the equations in the context of

alternate non-Riemannian spacetimes as well as other theories of gravity,

with a special mention on the equations in spacetimes with torsion

(Einstein--Cartan--Sciama--Kibble theory). Finally, we give an overview of

some recent applications of these equations in general relativity,

quantum field theory, string theory and the theory of relativisitic membranes.

We conclude with a summary and provide our own perspectives on directions of

future research.

Keywords. Raychaudhuri equations; general relativity; alternate theories of

gravity.

PACS Nos 04.20.-q; 04.50.+h; 11.25.-w