A comment on Liu and Yau's positive quasi-local mass

TL;DR

This paper demonstrates through examples that the Liu-Yau quasi-local mass can be strictly positive even in flat spacetime, challenging previous assumptions about its properties.

Contribution

It provides counterexamples showing the Liu-Yau quasi-local mass can be positive in flat spacetime, questioning its expected behavior.

Findings

Liu-Yau mass can be positive in flat spacetime

Counterexamples challenge previous positivity assumptions

Highlights limitations of existing quasi-local mass definitions

Abstract

With the aid of a simple family of examples, we show that the quasi-local mass defined by Kijowski and Liu and Yau, and shown by Liu and Yau to be positive, may be strictly positive for space-like, topologically spherical 2-surfaces in flat space-time.