Bounds for scalar waves 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 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.

arXiv comment16 pages, 1 figure. Published version

References in corpus (10)

• Quantum Probes of Spacetime Singularities
• Dynamics in Non-Globally-Hyperbolic Static Spacetimes II: General Analysis of Prescriptions for Dynamics
• Who's Afraid of Naked Singularities?
• Self-Similar Scalar Field Collapse: Naked Singularities and Critical Behaviour
• Convergence to a self-similar solution in general relativistic gravitational collapse
• Generalised hyperbolicity in singular space-times
• Scalar waves on a naked-singularity background
• Cauchy horizon stability in self-similar collapse: scalar radiation
• On the existence of self-similar spherically symmetric wave maps coupled to gravity
• Even perturbations of self-similar Vaidya space-time

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• Odd-parity perturbations of self-similar Vaidya spacetime
• Odd Parity Perturbations of the Self-Similar LTB Spacetime
• Gauge invariant perturbations of self-similar Lemaître-Tolman-Bondi spacetime: even parity modes with $l\ge 2$
• Gravitational collapse of a spherical scalar field
• Report on GRG18, Session A3, Mathematical Studies of the Field Equations