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

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• Steve Rogers
In summary: 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?In summary, the conversation discusses the topic of quasi-local mass or quasi-local energy and questions why it serves as a measure of gravitational energy. It also raises the issue of how to talk about gravitational energy in the context of general relativity, where gravity is viewed as a result of curved spacetime rather than a force.
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.

Steve Rogers said:
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.

vanhees71, Steve Rogers and Vanadium 50
PeterDonis said:
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.

vanhees71
Steve Rogers said:
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?

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

vanhees71

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