2023/05/01 by Ethan Sussman, Sussman, Ethan · 2 citations
Mathematics · Physics and Astronomy · #35B40. Secondary: 35P25 #35C20 #58J40 #58J47 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Primary: 35L05
paper · pdf · doi:10.48550/arxiv.2305.01119
openalex publication_date 2023/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study, fully microlocally, the propagation of massive waves on the octagonal compactification \mathbbO=[ℝ1,d;\mathscrI;1/2] of asymptotically Minkowski spacetime, which allows a detailed analysis both at timelike and spacelike infinity (as previously investigated using Parenti-Shubin-Melrose's sc-calculus) and, more novelly, at null infinity, denoted \mathscrI. The analysis is closely related to Hintz-Vasy's recent analysis of massless wave propagation at null infinity using the ``e,b-calculus'' on \mathbbO. We prove several elementary corollaries regarding the Klein-Gordon IVP. Our main technical tool is a fully symbolic pseudodifferential calculus, Ψde,sc(\mathbbO), the ``de,sc-calculus'' on \mathbbO. The `de' refers to the structure (``double edge'') of the calculus at null infinity, and the `sc' refers to the structure (``scattering'') at the other boundary faces. We relate this structure to the hyperbolic coordinates used in other studies of the Klein-Gordon equation. Unlike hyperbolic coordinates, the de,sc-boundary fibration structure is Poincaré invariant.