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The Raychaudhuri equation has seen extensive use in general relativity, most notably in the development of various singularity theorems.
R. P. Kerr, “Gravitational field of a spinning mass as an example of algebraically special metrics”, Phys. Rev. Lett. 11
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R. P. Kerr, “Gravitational collapse and rotation”, published in: Quasi-stellar sources and gravitational collapse: Including the proceedings of the First Texas Symposium on Relativistic Astrophysics , edited by Ivor Robinson, Alfred Schild, and E.L. Schücking (University of Chicago Press, Chicago, 1965), pages 99–102. The conference was held in Austin, Texas, on 16–18 December 1963
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S. W. Hawking and G. F. R. Ellis, The large scale structure of spacetime , (Cambridge University Press, England, 1973)
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C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation , (Freeman, San Francisco, 1973)
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R. M. Wald, General Relativity , (Chicago University Press, Chicago, 1984)
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K. S. Thorne, R. H. Price and D. A. Macdonald, Black holes: The membrane paradigm , (Yale University Press, New Haven, 1986)
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L. D. Landau and E. M. Lifschitz, The Classical Theory of Fields (Pergamon Press, Oxford, 2000), Chaps. 11, 12. See esp eq (105.22) on p 358 §105 [4th revised english edition.]
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S. M. Carroll, Spacetime and geometry: An introduction to general relativity , (Addison–Wesley, San Francisco, 2004)
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E. Poisson, A relativist’s toolkit: The mathematics of black hole mechanics , (Cambridge University Press, England, 2004)
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T. Padmanabhan, A. Patel, “Semiclassical quantization of gravity. 1. Entropy of horizons and the area spectrum”, [hep-th/0305165]
Cited in the paper.
T. Padmanabhan, “Gravitational entropy of static space-times and microscopic density of states”, Class. Quant. Grav. 21
2004
Later among the works it cites.
A. D. Rendall, Partial differential equations in general relativity , (Oxford University Press, England, 2008)
2008
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D. L. Wiltshire, M. Visser and S. M. Scott, The Kerr spacetime: Rotating black holes in general relativity , (Cambridge University Press, England, 2009)
2009
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2010
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T. Padmanabhan, A. Patel, “Role of horizons in semiclassical gravity: Entropy and the area spectrum”, [gr-qc/0309053]
Cited in the paper.
Cited in the paper.