John G Stalker and A Shadi Tahvildar-Zadeh 2004 Class. Quantum Grav. 21 2831 doi:10.1088/0264-9381/21/12/004
John G Stalker1 and A Shadi Tahvildar-Zadeh2
Show affiliationsWe obtain global spacetime weighted-L2 (Morawetz) and L4 (Strichartz) estimates for a massless chargeless spherically symmetric scalar field propagating on a super-extremal (overcharged) Reissner–Nordström background. To do this we first discuss the well-posedness of the Cauchy problem for scalar fields on non-globally hyperbolic manifolds, review the role played by the Friedrichs extension and go over the construction of the function spaces involved. We then show how to transform this problem to one about the wave equation on the Minkowski space with a singular potential, and prove that the potential thus obtained satisfies the various conditions needed in order for the estimates to hold.
04.20.Dw Singularities and cosmic censorship
04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 12 (21 June 2004)
Received 20 January 2004
Published 7 May 2004
John G Stalker and A Shadi Tahvildar-Zadeh 2004 Class. Quantum Grav. 21 2831
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