Special Seminar: The open problem of quasi-local mass in general relativity

Time and Location:

Einstein’s theory of general relativity is a geometric theory of gravitation. In this theory, matter sources induce curvature of spacetime through the Einstein field equations, which is a system of geometric partial differential equations. One of the fundamental open problems in geometric analysis and mathematical general relativity is the construction of a (universal) quasi-local mass to compute the mass of a finite region of spacetime. This has several applications in astrophysics, cosmology, and geometric analysis. One can use quasi-local mass to compute the binding energy of black hole mergers or compute the mass of finite regions of the universe using cosmological models. Moreover, one can use quasi-local mass to detect if there is a black hole in a region of spacetime. In this talk, we review some of the recent progress related to this open problem in the field of geometric analysis and mathematical relativity. Finally, we define a new gauge-independent quasi-local mass and energy with respect to the Minkowski spacetime and investigate its properties.