Curvature estimates for stable marginally trapped surfaces

TL;DR

This paper develops curvature estimates for stable marginally outer trapped surfaces in sliced space-times, providing bounds on shear based on intrinsic and extrinsic curvature, relevant for understanding dynamical horizons.

Contribution

It introduces new integral and sup-estimates for curvature and shear of marginally outer trapped surfaces in sliced space-times, applicable to physical scenarios like dynamical horizons.

Findings

Derived integral and sup-estimates for curvature

Bound shear in terms of intrinsic and extrinsic curvature

Applicable to dynamical horizons in physical contexts

Abstract

We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature of a slice containing the surface. These estimates are well adapted to situations of physical insterest, such as dynamical horizons.