Mass Aspect Function for Weakly Regular Asymptotically Hyperbolic Manifolds

Explore a mathematical relativity lecture on defining the mass aspect function for weakly regular asymptotically hyperbolic manifolds. Delve into the concept of mass in mathematical general relativity, focusing on manifolds asymptotic to hyperbolic space. Examine Wang's definition of mass using the mass aspect function and its relation to Chruściel and Herzlich's approach. Investigate joint work with Romain Gicquaud on extending these definitions to asymptotically hyperbolic manifolds with low regularity. Learn about using cut-off functions to define surface integrals and the mass aspect function as a distribution on the unit sphere for metrics with slower fall-off. Discuss the well-behaved nature of this mass definition under coordinate changes and the potential for proving positivity.