Well-posed geometric boundary data in General Relativity, II: twisted Dirichlet boundary data

Abstract

In this second work in a series, we prove the local-in-time well-posedness of the IBVP for the vacuum Einstein equations in general relativity with twisted Dirichlet boundary conditions on a finite timelike boundary. The boundary conditions consist of specification of the pointwise conformal class of the boundary metric, together with a scalar density involving a combination of the volume form of the bulk metric restricted to the boundary together with the volume form of the boundary metric itself.

Significant reworking of this series of papers on the IBVP in GR. This work is now second in the series. Results the same as in previous version, but some proofs corrected via the stronger use of energy estimates. Slight change to title. Additional improvements in exposition. 22 pages