Quasilocal Energy in General Relativity

TL;DR

This paper critiques the Wang-Yau quasilocal mass, showing it is ill-defined at spatial infinity and proposing an alternative that aligns with the ADM energy, enhancing the understanding of energy in general relativity.

Contribution

It introduces a new scheme for quasilocal mass that remains well-defined at infinity and converges to the ADM energy, improving upon previous definitions.

Findings

Wang-Yau mass is not well-defined at spatial infinity.

The proposed scheme asymptotes to the ADM energy.

The new scheme retains desirable properties of the Wang-Yau mass.

Abstract

We show that the quasilocal mass defined by Wang and Yau is not well-defined at spatial infinity. It approaches neither the ADM mass nor the ADM energy. We suggest an alternative scheme which retains all the desirable characteristics of the Wang-Yau mass and, in addition, asymptotes to the ADM energy at infinity.