Well-posed geometric boundary data in General Relativity, I: Conformal-mean curvature boundary data

2025/03/16 by An, Zhongshan, Anderson, Michael T. · 3 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2503.12599

Abstract

We study the local in time well-posedness of the initial boundary value problem (IBVP) for the vacuum Einstein equations in general relativity with geometric boundary conditions. For conformal-mean curvature boundary conditions, consisting of the conformal class of the boundary metric and mean curvature of the boundary, well-posedness does not hold without imposing additional angle data at the corner. When the corner angle is included as corner data, we prove well-posedness of the linearized problem in C^∞, where the linearization is taken at any smooth vacuum Einstein metric.

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