MG11 
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Abstract

Cosmological Singularities

This talk is divided into two parts. In the first part we discuss the issue of formulating and proving necessary and sufficient criteria for the existence of singular and complete spacetimes using conditions on the space gradient of the lapse function and the extrinsic curvature for general sliced spaces. We also discuss briefly the classification program of cosmological singularities. In the second part we focus on the issue of a dynamical definition of spacetime singularities and introduce the method of asymptotic splittings as a new tool to unravel the nature of cosmological spacetimes near their singularities. Several examples are discussed including the recently discovered sudden singularities.