Area inequalities for stable marginally trapped surfaces

TL;DR

This paper establishes inequalities relating area, angular momentum, and charges of stable marginally trapped surfaces in dynamical spacetimes, extending minimal surface tools to Lorentzian geometry for black hole horizon analysis.

Contribution

It introduces new area inequalities for marginally trapped surfaces in non-vacuum dynamical spacetimes with matter, broadening the understanding of black hole horizon properties.

Findings

Lower bounds for the area of trapping horizons.

Extension of minimal surface techniques to Lorentzian geometry.

Applicability to non-vacuum, dynamical spacetimes.

Abstract

We discuss a family of inequalities involving the area, angular momentum and charges of stably outermost marginally trapped surfaces in generic non-vacuum dynamical spacetimes, with non-negative cosmological constant and matter sources satisfying the dominant energy condition. These inequalities provide lower bounds for the area of spatial sections of dynamical trapping horizons, namely hypersurfaces offering quasi-local models of black hole horizons. In particular, these inequalities represent particular examples of the extension to a Lorentzian setting of tools employed in the discussion of minimal surfaces in Riemannian contexts.