Applications of Tractor Calculus in General Relativity - Part 3

Explore advanced applications of tractor calculus in general relativity in this 53-minute lecture by Dr. Jarosław Kopiński from the Center for Theoretical Physics PAS. Delve into how tractor calculus can be utilized to study specific classes of spacetimes with prescribed asymptotic behavior. Begin with an overview of basic tractor calculus concepts and their relation to conformal infinities. Learn about higher fundamental forms and their use in characterizing the conformal boundary of asymptotically de Sitter spacetimes. Investigate the geometric implications of spacetime possessing an initial isotropic singularity. Discover a general method for matching spacetimes in Penrose's Conformal Cyclic Cosmology model. This lecture is part of the bi-weekly seminar series for the Grieg collaboration project SCREAM, focusing on Cartan and parabolic geometries and their interactions with mechanical systems, integrable systems theory, and Penrose's Conformal Cyclic Cosmology programme.