Initial Data Sets That Do Not Satisfy the Regge-Teitelboim Conditions

Explore the intricacies of asymptotically Euclidean initial data sets in General Relativity through this one-hour talk by Melanie Graf at the Workshop on "Mathematical Relativity: Past, Present, Future" held at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the modeling of isolated systems at a given instant of time and the characterization of asymptotically Euclidean initial data sets. Examine the importance of asymptotic coordinates in ensuring the convergence of ADM-energy and the additional Regge-Teitelboim conditions required for BORT-center of mass convergence. Learn about the use of harmonic coordinates as a tool for verifying Regge-Teitelboim conditions and discover examples of asymptotically Euclidean initial data sets embedded in Schwarzschild that do not possess Regge-Teitelboim coordinates. Gain insights from Graf's joint work with Carla Cederbaum and Jan Metzger in this advanced exploration of mathematical relativity.