Hayward Quasilocal Energy of Tori

作     者：Xiaokai HE Naqing XIE Xiaokai HE;Naqing XIE

作者机构：School of Mathematics and StatisticsHunan First Normal UniversityChangsha 410205China School of Mathematical SciencesFudan UniversityShanghai 200433China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2022年第43卷第5期

页      面：773-784页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(No.11671089) the Natural Science Foundation of Hunan Province(No.2018JJ2073) the Key Project of Education Department of Hunan Province(No.21A0576) 

主　　题：Quasilocal energy Positivity Toroidal topology 

摘      要：In this paper, the authors show that one cannot dream of the positivity of the Hayward energy in the general situation. They consider a scenario of a spherically symmetric constant density star matched to the Schwarzschild solution, representing momentarily static initial data. It is proved that any topological tori within the star, distorted or not,have strictly positive Hayward energy. Surprisingly we find analytic examples of ‘thin’ tori with negative Hayward energy in the outer neighborhood of the Schwarzschild *** tori are swept out by rotating the standard round circles in the static coordinates but they are distorted in the isotropic coordinates. Numerical results also indicate that there exist horizontally dragged tori with strictly negative Hayward energy in the region between the boundary of the star and the Schwarzschild horizon.