Hertz potentials and asymptotic properties of massless fields

Abstract

In this paper we analyze Hertz potentials for free massless spin-s fields on the Minkowski spacetime, with data in weighted Sobolev spaces. We prove existence and pointwise estimates for the Hertz potentials using a weighted estimate for the wave equation. This is then applied to give weighted estimates for the solutions of the spin-s field equations, for arbitrary half-integer s. In particular, the peeling properties of the free massless spin-s fields are analyzed for initial data in weighted Sobolev spaces with arbitrary, non-integer weights.

Regularity assumptions corrected. Orthogonality condition eliminated

References in corpus (2)

• On the construction of a geometric invariant measuring the deviation from Kerr data
• Peeling of Dirac and Maxwell fields on a Schwarzschild background

Cited by in corpus (8)

• New identities for linearized gravity on the Kerr spacetime
• Mode stability on the real axis
• Symmetries of linearized gravity from adjoint operators
• Gluing for the constraints for higher spin fields
• Conformal scattering theory for the Dirac field on Kerr spacetime
• Cauchy and Goursat problems for the generalized spin zero rest-mass fields on Minkowski spacetime
• Asymptotic charges for spin-1 and spin-2 fields at the critical sets of null infinity
• Perturbations of Kerr with approximate Killing spinors -- Wave version