Is the universe finite or infinite? Where and how does it end? In this project, mathematicians explore how to describe the boundary of the universe based on Einstein's elegant geometric description of gravitation.
In the general theory of relativity, via Einstein's equation, gravitation in the universe is modeled via the curvature of spacetimes. Spacetimes can describe isolated systems (e.g., galaxies, a binary system, a black hole or star) of the real universe by imposing reasonable boundary conditions “at infinity”. When astronomers observe and interpret gravitational wave signals, for example, they make direct use of these hypothetical boundaries and their geometric features.
The current smoothness assumptions imposed on such mathematical boundary models, however, are typically not realized in the physical universe. This project aims at developing a novel geometric framework for analyzing nonsmooth conformal boundaries of spacetimes by exploiting and expanding recent approaches to nonsmooth Lorentzian geometry.