Dipartimento di

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Seminario / Drago

7 Maggio, ORE 14:45, AULA DOTTORATO

Nicolo' Drago (Dip. Fisica Universita' di Pavia)

Titolo: Wave propagation on Lorentzian manifolds with timelike boundary

Abstract: We discuss the existence of advanced and retarded propagators for the wave operator on static Lorentzian manifolds with timelike boundary. By means of spectral calculus the problem reduces to the study of the self-adjoint extensions of an associated elliptic operator on a Riemannian manifold with boundary. The latter can be addressed within the framework of boundary triples. These consists of the assignment of two surjective, trace operators from the domain of the adjoint of the elliptic operator into an auxiliary Hilbert space \mathsf{h}. Self-adjoint extensions of the underlying elliptic operator are then in one-to-one correspondence with self-adjoint operators \Theta on \mathsf{h}, which define a boundary condition for the original wave operator. We prove that for each such \Theta, it corresponds a unique advanced and retarded propagator. In addition we prove that these share the same structural property of the counterparts associated to the wave operator on a globally hyperbolic spacetime.

03 maggio 2018