English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We prove local existence of solutions to the Einstein--null dust system underpolarized $\mathbb U(1)$ symmetry in an elliptic gauge. Using in particular theprevious work of the first author on the constraint equations, we show that onecan identify freely prescribable data, solve the constraints equations, andconstruct a unique local in time solution in an elliptic gauge. Our mainmotivation for this work, in addition to merely constructing solutions in anelliptic gauge, is to provide a setup for our companion paper in which we studyhigh frequency backreaction for the Einstein equations. In that work, theelliptic gauge we consider here plays a crucial role to handle high frequencyterms in the equations. The main technical difficulty in the present paper, inview of the application in our companion paper, is that we need to build aframework consistent with the solution being high frequency, and thereforehaving large higher order norms. This difficulty is handled by exploiting areductive structure in the system of equations.

Einstein equations under polarized $\mathbb U(1)$ symmetry in an elliptic gauge