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arXiv · 1611.08755

Embeddings, immersions and the Bartnik quasi-local mass conjectures

Michael T. Anderson·Jeffrey L. Jauregui
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Abstract

Given a Riemannian 3-ball $(\bar B, g)$ of non-negative scalar curvature, Bartnik conjectured that $(\bar B, g)$ admits an asymptotically flat (AF) extension (without horizons) of the least possible ADM mass, and that such a mass-minimizer is an AF solution to the static vacuum Einstein equations, uniquely determined by natural geometric conditions on the boundary data of $(\bar B, g)$. We prove the validity of the second statement, i.e.~such mass-minimizers, if they exist, are indeed AF solutions of the static vacuum equations. On the other hand, we prove that the first statement is not true in general; there is a rather large class of bodies $(\bar B, g)$ for which a minimal mass extension does not exist.

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Michael T. Anderson, Jeffrey L. Jauregui. 2016-11-26. Embeddings, immersions and the Bartnik quasi-local mass conjectures. https://doi.org/10.1007/s00023-019-00786-3

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