Speaker
Description
The complexity and dynamical nature of spacetime, ruled by the Einstein field equations, make it hard (if not downright impossible) to find exact analytical solutions to most scenarios in General Relativity. This has lead physicists and mathematicians to explore, in the last few decades, the framework of the initial value problem. The Cauchy problem, as it is also called, consists of foliating spacetime into a set of (most commonly spacelike) hypersurfaces, also called leaves, which are then evolved through what is known as a propagation equation. Doing so requires an adaptation of the field equations and the introduction of new tensors, like the second fundamental form and the normal vector.
In this presentation we'll describe the mathematical framework behind the foliation of spacetime and formulate the IVP associated with General Relativity.
