Conformal Scattering of Maxwell Potentials

Abstract

We construct a complete conformal scattering theory for finite energy Maxwell potentials on a class of curved, asymptotically flat spacetimes with prescribed smoothness of null infinity and a non-zero ADM mass. In order to define the full set of scattering data, we construct a Lorenz-like gauge which makes the field equations hyperbolic and non-singular up to null infinity, and reduces to an intrinsically solvable ODE on null infinity. We develop a method to solve the characteristic Cauchy problem from this scattering data based on a theorem of Hörmander. In the case of Minkowski space, we further investigate an alternative formulation of the scattering theory by using the Morawetz vector field instead of the usual timelike Killing vector field.

arXiv comment48 pages; improved introduction; rough statements of main theorems included in introduction; expanded description of GHP formalism; theorems and definitions in sections 3 and 4 stated more clearly; to appear in Annales de l'Institut Fourier

References in corpus (19)

• Existence of non-trivial, vacuum, asymptotically simple space-times
• Asymptotics with a positive cosmological constant: I. Basic framework
• A scattering theory for the wave equation on Kerr black hole exteriors
• Stability of Minkowski space and polyhomogeneity of the metric
• A Scattering Theory for Linearised Gravity on the Exterior of the Schwarzschild Black Hole I: The Teukolsky Equations
• Conformal Scattering of Maxwell Fields on Reissner-Nordstrøm-de Sitter Black Hole Spacetimes
• A non-degenerate scattering theory for the wave equation on extremal Reissner-Nordstrom
• Initial value problems for wave equations on manifolds
• Conformal scattering for a nonlinear wave equation on a curved background
• A comparison of Ashtekar's and Friedrich's formalisms of spatial infinity
• Conformal Scattering and the Goursat Problem for Dirac Fields in the Interior of Charged Spherically Symmetric Black Holes
• Existence of exponentially growing finite energy solutions for the charged Klein-Gordon equation on the De Sitter-Kerr-Newman metric
• The Scattering Map on Oppenheimer--Snyder Spacetime
• Peeling on Kerr spacetime~:linear and non linear scalar fields
• Hörmander's method for the characteristic Cauchy problem and conformal scattering for a non linear wave equation
• Late-time asymptotics for geometric wave equations with inverse-square potentials
• Conformal scattering of the Maxwell-scalar field system on de Sitter space
• Conformal scattering theory for the linearized gravity fields on Schwarzschild spacetime
• Conformal scattering theory for the Dirac field on Kerr spacetime