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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