Positive Mass in General Relativity Without Energy Conditions

"[C]an general relativity discard negative mass solutions without the aid of quantum field theory? This would provide an alternative mechanism for the nonoccurrence of negative masses that does not rely on quantum theory at all. Hence, if true, it would show that gravity itself abhors negative masses, regardless of the matter content.

"A natural candidate for the role of a cosmic-weight watcher is the stability of solutions."

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"While general relativity cannot forbid an equilibrium solution with negative mass — after all any Lorentzian geometry is a solution to the Einstein field equations for the appropriate stress tensor — it may forbid stable solutions with negative mass. This happens in the cases considered in this work. While one can construct a negative-mass star, one cannot expect it to be stable under small hydrodynamical perturbations.

"Notice this gives a classical answer to a problem that may appear to be quantum in nature."

negative mass means anti gravity?