Cartan-Karlhede Algorithm and Cartan Invariants for Spacetimes - Part 3

Explore the Cartan-Karlhede algorithm and Cartan invariants for spacetimes in this 52-minute lecture by David McNutt from UiT The Arctic University of Norway. Delve into the classification of geometries and its significance in gravity theories, particularly general relativity and its modifications. Examine the background that led to the successful implementation of the Cartan algorithm for frame fields on manifolds, resulting in the Cartan-Karlhede algorithm for classifying solutions in General Relativity. Review the essential mathematical machinery required to implement the algorithm and understand how solution classification is carried out using Cartan invariants. Discover interesting applications of the Cartan-Karlhede algorithm and gain insights into this crucial aspect of differential geometry and its implications for various fields of study.