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- W4386556278 abstract "In this paper we generalise our previous results [1] concerning scattering on the exterior of collapsing dust clouds to the charged case, including in particular the extremal case. We analyse the energy boundedness of solutions $phi$ to the wave equation on the exterior of collapsing spherically symmetric charged matter clouds. We then proceed to define the scattering map on this spacetime, and look at the implications of our boundedness results on this map. More specifically, we first construct a class of spherically symmetric charged collapsing matter cloud exteriors, and then consider solutions to the wave equation with Dirichlet (reflective) boundary conditions on the surface of these clouds. We then show that the energy of $phi$ remains uniformly bounded going forwards or backwards in time, and that the scattering map is bounded going forwards but not backwards. Therefore, the scattering map is not surjective onto the space of finite energy on $mathcal{I}^+cupmathcal{H}^+$. Thus there does not exist a backwards scattering map from finite energy radiation fields on $mathcal{I}^+cupmathcal{H}^+$ to finite energy radiation fields on $mathcal{I}^-$ for these models. These results will be used to give a treatment of Hawking radiation in a companion paper [2]." @default.
- W4386556278 created "2023-09-09" @default.
- W4386556278 creator A5092829050 @default.
- W4386556278 date "2023-09-06" @default.
- W4386556278 modified "2023-10-16" @default.
- W4386556278 title "The Scattering Map on Collapsing Charged Spherically Symmetric Spacetimes" @default.
- W4386556278 doi "https://doi.org/10.48550/arxiv.2309.03025" @default.
- W4386556278 hasPublicationYear "2023" @default.
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