Existence, Regularity, and Properties of Generalized Apparent Horizons

Abstract

We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the existence of the outermost generalized apparent horizon in an initial data set and that it is outer area minimizing.

16 pages, thoroughly revised, no major changes, to appear in Comm. Math. Phys

References in corpus (3)

• On the Riemannian Penrose inequality in dimensions less than 8
• The area of horizons and the trapped region
• Nonexistence of Generalized Apparent Horizons in Minkowski Space

Cited by in corpus (13)

• The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight
• Bounds on area and charge for marginally trapped surfaces with cosmological constant
• The Merger of Small and Large Black Holes
• Initial data rigidity results
• On the mass aspect function and positive energy theorems for asymptotically hyperbolic manifolds
• On the geometry and topology of initial data sets with horizons
• Emergence of Apparent Horizon in Gravitational Collapse
• On the geodesic incompleteness of spacetimes containing marginally outer trapped surfaces
• Nonexistence of marginally trapped surfaces and geons in 2+1 gravity
• Outer entropy = Bartnik-Bray inner mass, and the gravitational ant conjecture
• The Positive Mass Theorem with Angular Momentum and Charge for Manifolds with Boundary
• On the topology of initial data sets with higher genus ends
• Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS