Dispersive and Strichartz estimates for Dirac equation in a cosmic string spacetime

TL;DR

This paper investigates the Dirac equation in a cosmic string spacetime, establishing selfadjoint extensions, explicit propagator kernels, and deriving dispersive and Strichartz estimates that differ from classical Euclidean results.

Contribution

It provides a detailed analysis of the Dirac operator in a cosmic string background, including explicit kernels and novel dispersive and Strichartz estimates.

Findings

Explicit kernel for the Dirac propagator in cosmic string spacetime

Dispersive estimates for the Dirac flow with and without weights

Strichartz estimates in a restricted set of indices different from Euclidean cases

Abstract

In this work we study the Dirac equation on the cosmic string background, which models a one--dimensional topological defect in the spacetime. We first define the Dirac operator in this setting, classifying all of its selfadjoint extensions, and we give an explicit kernel for the propagator. Secondly, we prove dispersive estimates for the flow, with and without weights. Finally, we prove Strichartz estimates for the flow in a sharp restricted set of indices, which are different from the classical Euclidean ones.