The Penrose inequality and apparent horizons

TL;DR

The paper constructs a specific spherically symmetric spacetime initial data set that challenges a common version of the Penrose inequality by showing a counterexample where mass is less than the horizon area term.

Contribution

It provides a counterexample to a widely accepted form of the Penrose inequality within spherically symmetric spacetimes.

Findings

Counterexample initial data set with M<√A/16π

Supports that the common Penrose inequality form is not universally valid

Does not contradict the true Penrose inequality

Abstract

A spherically symmetric spacetime is presented with an initial data set that is asymptotically flat, satisfies the dominant energy condition, and such that on this initial data $M<\sqrt{A/16\pi}$, where M is the total (ADM) mass and A is the area of the apparent horizon. This provides a counterexample to a commonly stated version of the Penrose inequality, though it does not contradict the ``true'' Penrose inequality.