Dr. Jarosław Kopiński (CTP PAS): Applications of tractor calculus in general relativity (Part III)
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2023-05-29

Dr. Jarosław Kopiński (Center for Theoretical Physics PAS).
Applications of tractor calculus in general relativity (Part I|I).
The goal of these lectures is to describe how tractor calculus
can be utilized to study specific classes of spacetimes with prescribed
asymptotic behaviour. To start, I will provide an overview of the basic
concepts of tractor calculus and how they relate to the description of
conformal infinities. Then, I will introduce the idea of higher
fundamental forms, which can be used to characterize the conformal
boundary of asymptotically de Sitter spacetimes. Next, I will explore
the geometric implications of the assumption that spacetime possesses an initial isotropic singularity. Finally, I will propose a general method
for matching spacetimes in Penrose's Conformal Cyclic Cosmology model.

This is a bi-weekly seminar for the Grieg collaboration project SCREAM: Symmetry, Curvature Reduction, and EquivAlence Methods, funded by the Norwegian Financial Mechanism 2014-2021. The registration number of the project is 2019/34/H/ST1/00636. 

The focus of the project is on a broad class of differential geometric structures known as Cartan and parabolic geometries, which include conformal, projective, CR, and ODE geometry, (2, 3, 5)-distributions, parabolic contact structures, and many more besides. Moreover, we explore the interaction of these structures with a variety of subjects such as mechanical systems and geometric robots, the theory of integrable systems, and Penrose's Conformal Cyclic Cosmology programme. 

More information can be found at www.cft.edu.pl/grieg.