TL;DR
The paper revisits Raychaudhuri's equation in the context of general relativity and argues for the necessity of a new quantum gravity analogue, highlighting ongoing challenges in understanding singularities.
Contribution
It draws parallels between Raychaudhuri's original work and current issues in loop quantum cosmology, emphasizing the need for a quantum gravity analogue of the equation.
Findings
Historical analysis of Raychaudhuri's role in singularity research
Identification of parallels between classical and quantum gravity issues
Call for new mathematical tools in quantum gravity
Abstract
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.
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