Conformal scattering of the Maxwell-scalar field system on de Sitter space

Abstract

We prove small data energy estimates of all orders of differentiability between past null infinity and future null infinity of de Sitter space for the conformally invariant Maxwell-scalar field system. This allows us to construct bounded and invertible, but nonlinear, scattering operators taking past asymptotic data to future asymptotic data. We also deduce exponential decay rates for solutions with data having at least two derivatives, and for more regular solutions discover an asymptotic decoupling of the scalar field from the charge. The construction involves a carefully chosen complete gauge fixing condition which allows us to control all components of the Maxwell potential, and a nonlinear Grönwall inequality for higher order estimates.

39 pages, typos corrected and bibliography updated

References in corpus (1)

• Stability and instability of the sub-extremal Reissner-Nordström black hole interior for the Einstein-Maxwell-Klein-Gordon equations in spherical symmetry

Cited by in corpus (5)

• A scattering theory for linear waves on the interior of Reissner-Nordström black holes
• Scattering from Infinity of the Maxwell Klein Gordon Equations in Lorenz Gauge
• Conformal scattering theory for the linearized gravity fields on Schwarzschild spacetime
• Conformal Scattering of Maxwell Potentials
• Conformal scattering theories for tensorial wave equations on Schwarzschild spacetime