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The Raychaudhuri equations: A brief review

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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.

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  1. Department of Physics and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur, 721 302, India

    Sayan Kar

  2. Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700 032, India

    Soumitra Sengupta

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  1. Sayan Kar
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Kar, S., Sengupta, S. The Raychaudhuri equations: A brief review. Pramana - J Phys 69, 49–76 (2007). https://doi.org/10.1007/s12043-007-0110-9

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