Singularity: Raychaudhuri Equation once again
نویسنده
چکیده
I first recount Raychaudhuri’s deep involvement with the singularity problem in general relativity. I then argue that precisely the same situation has arisen today in loop quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity. PACS numbers: 04.20.Jb, 04.2.Cv, 98.80 Dr 1 Singularity and AKR It would not be far from the truth to say that A. K. Raychaudhuri (AKR) had a fascinatingly engaging love affair with the notion of a spacetime singularity at the two ends of his research career. One of his early concerns was to construct a model of a collapsing homogeneous dust ball (he was unaware of Oppenheimer-Snyder collapse) and show that nothing prevented the ball from collapsing down to the centre r = 0 and thereby demystify the so called Schwarzschild singularity at r = 2M [1]. Then he addressed the most pertinent question of his time: is the cosmic singularity predicted by the FRW model an artifact of the homogeneity and isotropy of space or not? As he explained in his reminiscences [2], inspired by the famous Gödel solution, he was looking for a rotating non-singular solution without closed timelike lines. In the process, he discovered his celebrated equation [3] which made the singularity analysis free of these restrictions. That ultimately led to the powerful Hawking-Pensrose singularity theorems
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