# The well-posedness of the Cauchy problem for the Dirac operator on globally hyperbolic manifolds with timelike boundary

June 18, 2018

We consider the Dirac operator on globally hyperbolic manifolds with timelike boundary and show well-posedness of the Cauchy initial-boundary value problem coupled to MIT-boundary conditions. This is achieved by transforming the problem locally into a symmetric positive hyperbolic system, proving existence and uniqueness of weak solutions and then using local methods developed by Lax, Phillips and Rauch, Massey to show smoothness of the solutions. Our proof actually works for a slightly more general class of local boundary conditions.

Keywords:

Cauchy problem, Dirac operator, globally hyperbolic spacetimes with timelike boundary