On the stability of naked singularities
  We study the linearised stability of the nakedly singular negative mass Schwarzschild solution against gravitational perturbations. There is a one parameter family of possible boundary conditions at the singularity. We give a precise criterion for stability depending on the boundary condition. We show that one particular boundary condition is physically preferred and show that the spacetime is stable with this boundary condition. 
Gary W. Gibbons, Sean A. Hartnoll, Akihiro Ishibashi