Static vacuum Einstein metrics on bounded domains
Michael T Anderson
TL;DR
This paper investigates the existence and uniqueness of static vacuum Einstein metrics within bounded domains under specific boundary conditions involving prescribed boundary metric and mean curvature.
Contribution
It provides new results on the existence and uniqueness of solutions to the static vacuum Einstein equations with Bartnik boundary conditions.
Findings
Established conditions for existence of solutions.
Proved uniqueness under certain boundary data.
Characterized the solution space for static vacuum metrics.
Abstract
We study the existence and uniqueness of solutions to the static vacuum Einstein equations in bounded domains, satisfying the Bartnik boundary conditions of prescribed metric and mean curvature on the boundary.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Advanced Differential Geometry Research