We compute the graviton Kaluza-Klein spectrum on a gravity-dilaton background with a naked singularity for all possible boundary conditions at the singularity which are consistent with unitary evolution. We apply methods from nonrelativistic quantum mechanics with singular Schrödinger potentials. In general, the spectrum contains a tachyon, a sign of instability. Only for a particular boundary condition at the singularity is the spectrum free of tachyons. In this case, the lowest-lying graviton mode is massless. We argue that this result will also hold for other backgrounds with similar geometry near the curvature singularity. We complete our study with a brief discussion on radion perturbations and the Higgs mechanism on this singular background. © 2013 American Physical Society.
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|Publication status||Published - 12 Nov 2013|