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Explore the evolution of geometric invariants in asymptotically hyperboloidal initial data sets through this 21-minute conference lecture from the Workshop on "Hyperboloidal Foliations and their Application" at the Erwin Schrödinger International Institute for Mathematics and Physics. Discover joint research with Saradha Senthil Velu that examines the concepts of energy and linear momentum using hyperboloidal time functions to describe evolution. Learn about the innovative concept of E–P chargeability—a crucial property of initial data sets that ensures well-defined energy and momentum charges—and understand the proof demonstrating this property's preservation throughout the chosen evolution. Examine the derivation of energy-loss and linear momentum-loss formulae that recover the classical results of Bondi, Sachs, and Metzner while operating under weaker asymptotic assumptions. Understand how this approach differs from methods using conformal compactifications by working directly at the initial data set level, and gain insights into ongoing developments and current research directions in this field of mathematical physics.
