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Conformal scattering of the wave equation in the Vaidya spacetime

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arxiv 2405.08659 v1 pith:KMGY7JQC submitted 2024-05-14 gr-qc math-phmath.MP

Armand Coudray This is my paper · ORCID
classification gr-qcmath-phmath.MP
keywords operatorscalarscatteringspacetimeconformalequationestimatesfield
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We construct the conformal scattering operator for the scalar wave equation on the Vaidya spacetime using vector field methods. The spacetime we consider is Schwarzschild, near both past and future timelike infinities, in order to use existing decay results for the scalar field, ensuring our energy estimates. These estimates guarantee the injectivity of the trace operator and the closure of its range. Finally, we solve a Goursat problem for the scalar waves on null infinities, demonstrating that the range of the trace operator is dense. Consequently, this implies that the scattering operator is an isomorphism.

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  1. A generalization of the Fredenhagen-Haag derivation of Hawking radiation for a class of Vaidya space-times

    gr-qc 2026-08 conditional novelty 7.0 of 10

    A rigorous finite-window detector-response bound for massless scalar fields on Vaidya spacetimes, comparing the response to a frozen Schwarzschild thermal reference with explicit error terms.

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