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Hayward Quasilocal Energy of Tori

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Abstract

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 horizon. These 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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hunan First Normal University, Changsha, 410205, China

    Xiaokai He

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Naqing Xie

Authors
  1. Xiaokai He
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  2. Naqing Xie
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Corresponding authors

Correspondence to Xiaokai He or Naqing Xie.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11671089), the Natural Science Foundation of Hunan Province (No. 2018JJ2073) and the Key Project of Education Department of Hunan Province (No. 21A0576).

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He, X., Xie, N. Hayward Quasilocal Energy of Tori. Chin. Ann. Math. Ser. B 43, 773–784 (2022). https://doi.org/10.1007/s11401-022-0357-y

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  • DOI: https://doi.org/10.1007/s11401-022-0357-y

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