Hayward Quasilocal Energy of Tori

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