Wellposedness of the initial boundary value problem for the conformal field equations

TL;DR

This paper formulates and proves the well-posedness of the initial boundary value problem for conformal Einstein field equations using a gauge based on conformal geodesics, with specific boundary conditions.

Contribution

It introduces a new formulation of the IBVP for conformal Einstein equations with boundary conditions aligned with conformal geodesics and proves well-posedness and constraint propagation.

Findings

Established well-posedness for a class of boundary conditions.

Identified boundary conditions compatible with conformal geodesic gauge.

Proved the propagation of constraints in the formulated IBVP.

Abstract

We provide a formulation of the initial boundary value problem for Friedrich's extended conformal Einstein field equations in which boundary data is prescribed on a timelike hypersurface located at a finite position in the spacetime. Our construction relies on a gauge based on the properties of conformal geodesics and requires the the boundary is ruled by timelike conformal geodesics. The consequences of this assumption on the timelike boundary are analysed and we identify a subset of maximally dissipative boundary conditions which are consistent with this assumption. For this class of consistent boundary conditions we establish the wellposedness of the initial boundary value problem and prove the propagation of the constraints.