The area of horizons and the trapped region

TL;DR

This paper investigates the properties and boundaries of marginally trapped surfaces in Einstein's equations, providing area estimates and a new surgery method to better understand the trapped region in spacetime.

Contribution

It introduces a novel surgery construction for marginal surfaces and characterizes the boundary of the trapped region in Cauchy data sets.

Findings

Proved an area estimate for outermost marginally trapped surfaces.

Developed a new surgery technique for marginal surfaces.

Characterized the boundary of the trapped region.

Abstract

This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for marginal surfaces. These results are applied to characterize the boundary of the trapped region.