Positivity of Mass for Asymptotically Hyperbolic Initial Data Sets - IPAM at UCLA

Explore a 38-minute lecture on the positivity of mass for asymptotically hyperbolic initial data sets in Einstein's equations. Delve into the mathematical foundations of hyperboloidal initial data modeled on the upper unit hyperboloid in Minkowski spacetime. Examine the motivation behind studying this type of initial data, including its relevance to proving the positivity of Bondi mass in isolated physical systems. Investigate the Schoen and Yau approach from 1982, which builds upon their 1981 proof of the positive mass theorem for asymptotically Euclidean initial data sets. Understand the key role of the Jang equation in deforming spacelike hypersurfaces to capture Bondi mass. Learn how this method applies to prove mass positivity in asymptotically hyperbolic initial data sets within the non-radiating regime. Gain insights from Anna Sakovich of Uppsala University in this presentation at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation.