Séminaire de Géométrie

Invariant geometry of gravitational waves

1180 (Bât E2)


Bât E2

Site Grandmont

The existence of gravitational waves is one of the prediction, now empirically validated, of Einstein's General Relativity. The underlying mathematical model for this predication is a class of Einstein Lorentzian manifolds dubbed "Asymptotically flat space-times". These are particular case of conformally compact manifolds, the presence of gravitational waves being geometrically encoded in their asymptotics (i.e at the conformal boundary).

I will review some of the definitions and classical results associated to asymptotically flat-space times:  with an emphasis on the intertwined aspects of both geometry and physics. I will then show how a generalisation of the tractor calculus from conformal geometry can be used to invariantly and intrinsically encode gravitational radiations as an "extra" layer of geometry at the conformal boundary: they amounts to a choice of Tractor connection (these are a particular case of Cartan connections). More precisely, a non-vanishing tractor curvature correspond to the presence of gravitational radiations while the moduli space of flat connections is physically associated to the so-called "degeneracy of gravity vacua".