Instability of the negative mass Schwarzschild naked singularity,

G. DOTTI Y R. GLEISER

CLASSICAL AND QUANTUM GRAVITY

IOP PUBLISHING LTD

Año: 2006 vol. 23 p. 5063 - 5078

0264-9381

We study the negative mass Schwarzschild spacetime, which has a nakedsingularity, and show that it is perturbatively unstable. This is achievedby first introducing a modification of the well-known Regge–Wheeler–Zerilli approach to black hole perturbations to allow for the presence of a‘kinematic’ singularity that arises for negative masses, and then exhibiting exactexponentially growing solutions to the linearized Einstein’s equations. Theperturbations are smooth everywhere and behave nicely around the singularityand at infinity. In particular, the first-order variation of the scalar invariantscan be made arbitrarily small everywhere as compared to the zeroth orderterms. Our approach is also compared to a recent analysis that leads to adifferent conclusion regarding the stability of the negative mass Schwarzschildspacetime. We also comment on the relevance of our results to the stability ofa more general negative mass, nakedly singular spacetimes.