Abstract:

In 1981, Schoen-Yau proved the spacetime positive energy theorem by reducing it to the time-symmetric (Riemannian) case using the Jang equation. To acquire solutions to the Jang equation, they introduced a family of regularized equations and took the limit of regularized solutions, whereas a sequence of regularized solutions could blow up in some bounded regions enclosed by apparent horizons. They analyzed the blowup behavior near but outside of apparent horizons, but what happens inside remains unknown. In this talk, we will discuss the blowup behavior inside apparent horizons through two common geometric treatments: dilation and translation. We will also talk about the relation between the limits of regularized solutions and constant null expansion surfaces.