Conformally Covariant Systems of Wave Equations and their Equivalence to Einstein’s Field 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.