Dr. Jarosław Kopiński (CTP PAS): Applications of tractor calculus in general relativity (Part I)
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2023-04-24

Dr. Jarosław Kopiński (Center for Theoretical Physics PAS).
Applications of tractor calculus in general relativity (Part 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.