Scalar waves on a naked-singularity background

Details Scalar waves on a naked-singularity background Scalar waves on a naked-singularity background

2004-01-04

arxiv.org/abs/gr-qc/0401011v3

Class.Quant.Grav. 21 (2004) 2831-2848

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/21/12/004

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.

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