Centre de Physique Théorique


Friday 13 March 2020

14h00 – 15h00, CPT, Amphi 5

Intrinsic conformal geometry of null-infinity and its gravitational wave

Yannick Herfray, Université Libre de Bruxelles

Our best current model for describing gravitational waves, as for example measured in LIGO, is a family of solution to vacuum Einstein equations called asymptotically-flat space-times. Observers are then taken to be situated "at null-infinity" and, since the seminal work of Bondi’s group and Sachs, gravitational waves are related to the presence of a certain tensor, the "asymptotic shear", appearing in an asymptotic expansion away from null-infinity. Intuitively the presence of gravitational waves should correspond to the presence of some extra geometrical data at null-infinity but such a geometrisation however proved to be quite elusive. This is essentially because the geometry of null-infinity is of conformal nature which is notoriously tedious to work with. I will review these well-known facts and show how modern methods in conformal geometry (namely tractor calculus) can be adapted to the degenerate conformal geometry of null-infinity to encode the presence of gravitational waves in a completely geometrical way: the "asymptotic shear" is proved to be in 1-1 correspondence with choices of tractor connection, gravitational radiation is invariantly described by the tractor curvature and "soft-modes" of the vacuum correspond to the degeneracy of flat tractor connections.