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 blowup regularized
solutions and constant expansion surfaces.