Carroll, Cotton and Ehlers

Abstract: Carroll geometries emerge as conformal boundaries of asymptotically flat spacetimes and have come to the forefront with the advent of flat holography. I will introduce these tools and show how they are used for unravelling the boundary manifestation of Ehlers' hidden Möbius symmetry present in four-dimensional Ricci-flat spacetimes that enjoy a time-like isometry. This is achieved in a designated gauge, where the three-dimensional Carrollian nature of the null conformal boundary is manifest and covariantly implemented. The action of the Möbius group is local on the space of Carrollian boundary data. Among these data, the Carrollian Cotton tensor plays a prominent role both in the Möbius electric/magnetic duality and for the determination of charges.

A New Weyl Invariant Theory of Gravity

Abstract:

The Asymptotic Structure of Flat Spacetimes

Abstract: One of the most impressive achievements of theoretical physics is the “principle of least action” of classical mechanics, where a substantial number of phenomena can be described by just a single statement: the action must be stationary under arbitrary variations of the dynamical variables, with initial and final condition that must be held fixed. Therefore, the powerful formulation of classical and quantum mechanics based in the action, needs to be supplemented with a proper treatment of boundary conditions at infinity. This issue is of vital importance in the case of theories where the sufficiently rapidly decay of the fields at infinity is not a valid assumption. For example, the asymptotic symmetry analysis of General Relativity leads to the renowned BMS (Bondi-van der Burg-Metzner-Sachs) group, which corresponds to a fundamental piece in the understanding of the infrared dynamics of gravitational interactions. In this talk, the asymptotic structure of flat spacetimes will be discussed, focusing on the case of gravity and its interactions, starting in three spacetime dimensions and then discussing the higher dimensional case.