On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n + 2)-dimensional static and spherically symmetric spacetimes. They are related to the properties of the underlying spatial part of the wave operator, one of which...
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| Autores principales: | , , |
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
2013
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/98574 https://ri.conicet.gov.ar/11336/23632 http://iopscience.iop.org/article/10.1088/0264-9381/30/23/235014 |
| Aporte de: |
| Sumario: | We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n + 2)-dimensional static and spherically symmetric spacetimes. They are related to the properties of the underlying spatial part of the wave operator, one of which being the standard essentially self-adjointness. However, in many examples the spatial part of the wave operator turns out to be not essentially self-adjoint, but it does satisfy a weaker property that we call here quasi-essentially self-adjointness, which is enough to ensure the desired well-posedness. This is why we also characterize this second property. We state abstract results, then general results for a class of operators encompassing many examples in the literature, and we finish with the explicit analysis of some of them. |
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