, Volume 69, Issue 1, pp 49–76

The Raychaudhuri equations: A brief review

  • Sayan Kar
  • Soumitra Sengupta

DOI: 10.1007/s12043-007-0110-9

Cite this article as:
Kar, S. & Sengupta, S. Pramana - J Phys (2007) 69: 49. doi:10.1007/s12043-007-0110-9


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.


Raychaudhuri equations general relativity alternate theories of gravity 


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Copyright information

© Indian Academy of Sciences 2007

Authors and Affiliations

  • Sayan Kar
    • 1
  • Soumitra Sengupta
    • 2
  1. 1.Department of Physics and Centre for Theoretical StudiesIndian Institute of TechnologyKharagpurIndia
  2. 2.Department of Theoretical PhysicsIndian Association for the Cultivation of ScienceJadavpur, KolkataIndia

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