The Cauchy problem for Lorentzian Dirac operators under non-local boundary conditions
Differential Geometry
2022-10-28 v1 Analysis of PDEs
Abstract
Non-local boundary conditions, such as the Atiyah-Patodi-Singer (APS) conditions, for Dirac operators on Riemannian manifolds are well understood while not much is known for such operators on spacetimes with timelike boundary. We define a class of Lorentzian boundary conditions that are local in time and non-local in the spatial directions and show that they lead to a well-posed Cauchy problem for the Dirac operator. This applies in particular to the APS conditions imposed on each level set of a given Cauchy temporal function.
Cite
@article{arxiv.2210.15052,
title = {The Cauchy problem for Lorentzian Dirac operators under non-local boundary conditions},
author = {Christian Baer and Penelope Gehring},
journal= {arXiv preprint arXiv:2210.15052},
year = {2022}
}
Comments
37 pages, 4 figures