Scalar waves on a naked-singularity background

Abstract

We obtain global space-time weighted-L^2 (Morawetz) and L^4 (Strichartz) estimates for a massless chargeless scalar field propagating on a super-extremal (overcharged) Reissner-Nordstrom background. We begin by discussing the question of well-posedness of the Cauchy problem for scalar fields on non-globally hyperbolic manifolds and the role played by the Friedrichs extension, go over the construction of the function spaces involved, show how to transform the problem to one about the wave equation on the Minkowski space with a singular potential, and finally prove that the potential thus obtained satisfies the various conditions needed in order for the estimates to hold.

20 pages, 2 figures. final version, to appear in Classical and Quantum Gravity. Includes minor corrections, additional footnotes and references

References in corpus (3)

• Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates
• Dynamics in Stationary, Non-Globally Hyperbolic Spacetimes
• A Compactness Criterion for Real Plane Algebraic Curves

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