GT1 - Cosmological Singularities |
Speaker_ |
Nolan, Brien |
Talk _ |
Bounds for scalar waves and linear perturbations on self-similar naked-singularity backgrounds |
Abstract _ |
The stability of naked singularities in self-similar collapse is probed using scalar waves. It is shown that the multipoles of a minimally coupled massless scalar field propagating on a spherically symmetric self-similar background space-time admitting a naked singularity maintain finite $H^{1,2}$ norm as they impinge on the Cauchy horizon. It is also shown that each multipole obeys a pointwise bound at the horizon, as does its locally observed energy density. $H^{1,2}$ and pointwise bounds are also obtained for the multipoles of a minimally coupled massive scalar wave packet. We discuss the extension of these results to odd-parity linear perturbations of the space-time. |