High Energy Theory Seminar: Jelle Hartong

Title: The Geometry of Gravitational Radiation

 

Abstract: This talk concerns asymptotically flat vacuum solutions of GR in 4 spacetime dimensions. The asymptotics of such metrics is quite intricate and depends on how we approach infinity. If we follow null geodesics we end up at future null infinity. This is where massless fields, including gravitational radiation ends up. In this talk we will study the metric near future null infinity with an emphasis on geometrical structures that emerge in that part of the spacetime.

Future null infinity of an asymptotically flat spacetime is a conformal Carroll manifold. I will not assume any familiarity with Carroll geometry and explain the relevant geometrical notions as we go along. We will consider asymptotic solutions to the 4D vacuum Einstein equations where future null infinity is endowed with the most general Carroll metric data that is allowed by the Einstein equations. This can be used to define an energy-momentum tensor (EMT) at future null infinity by varying a suitably renormalised action with respect to the boundary Carroll metric data. It is shown that the Ward identities obeyed by this boundary EMT agree with the Bondi loss equations that describe the loss of energy and momentum due to the emission of gravitational waves. The metric near future null infinity can be formulated in terms of a Cartan geometry based on the conformal Carroll algebra. The non-vanishing curvatures of said algebra dictate how radiative the spacetime is. For example, the vacuum degeneracy is described by a flat conformal Carroll connection. We will see that the Bondi loss equations can be rewritten as flux-balance laws where the fluxes are determined by the Cartan geometry for the conformal Carroll algebra.