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Bounds for scalar waves on self-similar naked-singularity backgrounds

Brien C. Nolan
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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 spacetime admitting a naked singularity maintain finite $L^2$ 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. $L^2$ and pointwise bounds are also obtained for the multipoles of a minimally coupled massive scalar wave packet.

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Brien C. Nolan. 2006-06-19. Bounds for scalar waves on self-similar naked-singularity backgrounds. https://doi.org/10.1088/0264-9381%2F23%2F13%2F015

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