Blowup of Jang's equation at outermost marginally trapped surfaces

Abstract

The aim of this paper is to collect some facts about the blowup of Jang's equation. First, we discuss how to construct solutions that blow up at an outermost MOTS. Second, we exclude the possibility that there are extra blowup surfaces in data sets with non-positive mean curvature. Then we investigate the rate of convergence of the blowup to a cylinder near a strictly stable MOTS and show exponential convergence near a strictly stable MOTS.

15 pages. This revision corrects some typos

References in corpus (3)

• Local existence of dynamical and trapping horizons
• The area of horizons and the trapped region
• The Jang equation, apparent horizons, and the Penrose inequality

Cited by in corpus (8)

• The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight
• Codimension two marginally trapped submanifolds in Robertson-Walker spaces
• Density and positive mass theorems for initial data sets with boundary
• On the geometry and topology of initial data sets with horizons
• Emergence of Apparent Horizon in Gravitational Collapse
• A Penrose-Like Inequality with Charge
• On blow-up solutions of the Jang equation in spherical symmetry
• Some Remarks on Wang-Yau Quasi-Local Mass