Positive energy theorem implies constraints on static steller models
  Using the positive energy theorem, we derive some constraints on static steller models in asymptotically flat spacetimes in a general setting without imposing spherical symmetry. We show that there exist no regular solutions under certain conditions on the equation of state. As the contraposition, we obtain some constraints on the pressure and adiabatic index. 
Tetsuya Shiromizu, Hirotaka Yoshino