2025/12/18 by Izak Oltman, Oltman, Izak, Ben Pineau +1
Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #Pulsars and Gravitational Waves Research
paper · pdf · doi:10.48550/arxiv.2512.16054
openalex publication_date 2025/12/18 · openalex created_date 2025/12/21 · openalex updated_date 2026/07/28
This paper proposes a Poisson formula for the wave propagator of the Schwarzschild--de Sitter (SdS) metric. That is done by proving a Poisson formula relating wave propagators and scattering resonances for a class of non-compactly supported potentials on the real line. That class includes the Regge-Wheeler potentials obtained from separation of variables for SdS. The novelty lies in allowing non-compact supports -- all exact Poisson formulae of Lax-Phillips, Melrose, and other authors required compactness of the support of the perturbation. A key feature of the analysis is the presence of an exceptional class of potentials for which outgoing solutions may vanish at certain non-resonant frequencies. We identify and describe this class, which we call the resonant condition.