Artículos de revistas
On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
Fecha
2013-10Registro en:
Gamboa Saravi, Ricardo Enrique; Sanmartino, Marcela; Tchamitchian, Philippe ; On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes; IOP Publishing; Classical and Quantum Gravity; 30; 23; 10-2013; 235014-235044
0264-9381
CONICET Digital
CONICET
Autor
Gamboa Saravi, Ricardo Enrique
Sanmartino, Marcela
Tchamitchian, Philippe
Resumen
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.