Crete Gravity Days

We will review some properties of boundaries to spacetime both in a Riemannian and Lorentzian setting for Einstein’s gravity. We will outline some surprising new results about what boundary conditions allow a good behaviour (well-posedness) for the bulk theory.

This talk concerns the existence and asymptotic behaviour of solutions to the relativistic Euler equations near big bang singularities. I will explain how suitable rescalings and energy estimates, organised within a Fuchsian framework, yield rigorous control of the singular evolution. Applications to cosmological backgrounds will illustrate the role of geometric anisotropy and the equation of state, including recent results in the extremely tilted regime.

The solution space of General Relativity is filled with a rich variety of behavior. Spacetimes at or close to the threshold of black hole formation are of particular interest because they (potentially) serve as counterexamples to the cosmic censorship conjectures. In spherical symmetry, where dynamics are necessarily driven by a choice of matter, such solutions are furthermore known to exhibit a surprising amount of structure, called “Critical Phenomena in Gravitational Collapse.” Yet in axisymmetry and beyond, the story appears to become much more subtle. In this presentation I will give an overview of the topic, up to and including discussion of state-of-the-art results on the black hole threshold in vacuum gravity in axisymmetry. Special attention will be given to the open challenges we face, especially in drawing reliable conclusions from numerical evolutions as symmetry is discarded.