2006/04/30 by Reinaldo J. Gleiser, Gustavo Dotti · 3 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #gr-qc
paper · pdf · doi:10.1088/0264-9381/23/15/021
published as Class.Quant.Grav. 23 (2006) 5063-5078 · 15 pages
arxiv created 2006/05/29 · openalex publication_date 2006/07/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
We study the negative mass Schwarzschild spacetime, which has a naked singularity, and show that it is perturbatively unstable. This is achieved by 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 exact exponentially growing solutions to the linearized Einstein's equations. The perturbations are smooth everywhere and behave nicely around the singularity and at infinity. In particular, the first-order variation of the scalar invariants can be made arbitrarily small everywhere as compared to the zeroth order terms. Our approach is also compared to a recent analysis that leads to a different conclusion regarding the stability of the negative mass Schwarzschild spacetime. We also comment on the relevance of our results to the stability of a more general negative mass, nakedly singular spacetimes.