240507 Jack Borthwick

May 7, 2024

Title: Asymptotic structures at timelike infinity and projective geometry

Speaker: Jack Borthwick (McGill University, Montréal)

Scri, or null-infinity, is nowadays a fundamental concept for discussing the asymptotic structure of space time. On asymptotically flat manifolds, whose asymptotic structure is modelled on the conformal compactification of Minkowski space time, scri is topologically a line bundle over a sphere. There is, however, another way to compactify Minkowski spacetime based on projective geometry. This construction leads to richer regions in the time/space like regions of the boundary at infinity than the conformal one but the null region is of codimension 2. Roughly, we've lost the fibres of the line bundle. Ashtekar's exploration of the notion of asymptotic flatness at spacelike infinity also suggests that it is also meaningful to consider a line bundle over the other regions of infinity in the projective compactification. In this talk, we consider this from a geometric perspective: what are these line bundles? Is it possible to equip them with geometric structures in a natural way? This talk is based on joint ongoing work with Yannick Herfray (Univ. Tours)

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