D. McNutt (UiT The Arctic University):Cartan-Karlhede algorithm and Cartan invariants for spacetimes
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2023-02-27

David McNutt (UiT The Arctic University of Norway).
Cartan-Karlhede algorithm and Cartan invariants for spacetimes.
The classification of geometries is an important and interesting question in mathematics in itself. In gravity theories, like general relativity and its modifications, finding and enumerating solutions to the associated field equation gives a new motivation for the classification problem. In this talk I will discuss the background that led to the successful implementation of the Cartan algorithm for frame fields on a manifold to a classification algorithm for solutions in General relativity, known as the Cartan-Karlhede algorithm. In particular, I will review the necessary mathematical machinery required to implement the algorithm, and how classification of solutions is carried out using a set of invariants generated by the algorithm, known as  Cartan invariants. Lastly, I will discuss some interesting applications of the Cartan-Karlhede algorithm.

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 in www.cft.edu.pl/grieg.