Chen-Nester-Tung quasi-local energy and Wang-Yau quasi-local mass

TL;DR

This paper explores the relationship between Chen-Nester-Tung quasi-local energy and Wang-Yau quasi-local mass, analyzing their properties and variations in Kerr-like spacetimes, and generalizing previous results on their coincidence.

Contribution

It establishes a connection between CNT quasi-local energy and WY quasi-local mass, computes second variations in Kerr-like spacetimes, and generalizes earlier coincidence results.

Findings

CNT energy is related to WY mass.

Second variation shows saddle points in Kerr-like spacetimes.

Generalizes previous coincidence results to broader spacetimes.

Abstract

In this paper, we show that the Chen-Nester-Tung (CNT) quasi-local energy is closely related to the Wang-Yau (WY) quasi-local mass. As a particular example, we compute the second variation of the CNT quasi-local energy for axially symmetric Kerr-like spacetimes with axially symmetric embeddings at the obvious critical point (0,0) and find that it is a saddle critical point in most of the cases. Also, as a byproduct, we generalize a previous result about the coincidence of CNT quasi-local energy and Brown-York mass for Kerr-like spacetimes by Tam and the first author to general spacetimes.