Penelope Gehring
Non-local boundary conditions – for example the Atiyah–Patodi–Singer (APS) conditions – for Dirac operators on Riemannian manifolds are rather well-understood, while not much is known for such operators on Lorentzian manifolds. Recently, Bär and Strohmaier and Drago, Große, and Murro introduced APS like conditions for the spin Dirac operator on Lorentzian manifolds with spacelike and timelike boundary, respectively. While Bär and Strohmaier showed the Fredholmness of the Dirac operator with these boundary conditions, Drago, Große, and Murro proved the well-posedness of the corresponding initial boundary value problem under certain geometric assumptions.
In this talk, we will follow the footsteps of the latter authors and discuss whether the APS-like conditions for Dirac operators on Lorentzian manifolds with timelike boundary can be replaced by more general conditions such that the associated initial boundary value problems are still well-posed.
