Quasi-local mass as a measure of the gravitational energy?

[Steve Rogers]

TL;DR Summary

How can we talk about the gravitational energy without considering it as a force field?

I'm self-studying the mathematical aspects of quasi-local mass, or quasi-local energy (e.g. Hawking energy), and a fundamental question has been lingering in my mind for a long time: why does quasi-local mass provide us with a measure of the gravitational energy? In general relativity, gravitation is seen as a consequence of the curved spacetime instead of a force in classical mechanics. If so, how can we talk about its energy without considering it as a force field? Thank you.

 

[PeterDonis]

quasi-local mass, or quasi-local energy

Please give a specific reference for where you are getting this from. Without a specific reference we do not have a valid basis for discussion.

 

[Steve Rogers]

Please give a specific reference for where you are getting this from. Without a specific reference we do not have a valid basis for discussion.

Hello, a quick reference for this topic can be found on arXiv, as follows.
https://arxiv.org/abs/1510.02931

I guess the term "quasi-local mass" is more familiar to people working on mathematical relativity or mathematical physics, such as Shing-Tung Yau and Robert Geroch.

Thank you for replying.

 

[PeterDonis]

a quick reference for this topic can be found on arXiv, as follows.

Thanks for the reference. Can you point out which particular part of it is the basis for your question?

why does quasi-local mass provide us with a measure of the gravitational energy?