Stability of naked singularities and algebraically special modes

Abstract

We show that algebraically special modes lead to the instability of naked singularity spacetimes with negative mass. Four-dimensional negative-mass Schwarzschild and Schwarzschild-de Sitter spacetimes are unstable. Stability of the Schwarzschild-anti-de Sitter spacetime depends on boundary conditions. We briefly discuss the generalization of these results to charged and rotating singularities.

Comments: 6 pages. ReVTeX4. v2: Minor improvements and extended discussion on boundary conditions. Version to appear in Phys. Rev. D