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.
- Pub Date:
- July 2007
- Raychaudhuri equations;
- general relativity;
- alternate theories of;
- General Relativity and Quantum Cosmology
- 35 pages, two figures, to appear in the special issue of Pramana dedicated to the memory of A. K. Raychaudhuri