Conformally covariant systems of wave equations and their equivalence to Einstein's field equations

TL;DR

This paper develops two conformally covariant wave equation systems derived from Friedrich's conformal field equations, demonstrating their equivalence to Einstein's vacuum equations and applying this to initial value problems at null infinity.

Contribution

It introduces two new wave equation systems based on Friedrich's conformal approach and proves their equivalence to Einstein's equations under certain constraints.

Findings

Two alternative wave systems derived from conformal field equations.

Equivalence of these systems to Einstein's vacuum equations under constraints.

Reduction of characteristic initial value problem at null infinity to wave equations.

Abstract

We derive, in 3+1 spacetime dimensions, two alternative systems of quasi-linear wave equations, based on Friedrich's conformal field equations. We analyse their equivalence to Einstein's vacuum field equations when appropriate constraint equations are satisfied by the initial data. As an application, the characteristic initial value problem for the Einstein equations with data on past null infinity is reduced to a characteristic initial value problem for wave equations with data on an ordinary light-cone.