On the Bartnik conjecture for the static vacuum Einstein equations

Abstract

We prove that given any smooth metric $\gamma$ and smooth positive function $H$ on $S^2$, there is a constant $\lambda >0$, depending on $(\gamma ,H)$, and an asymptotically flat solution $(M,g,u)$ of the static vacuum Einstein equations on $M={\mathbb{R}}^3\setminus B^3$, such that the induced metric and mean curvature of $(M,g,u)$ at $\partial M$ are given by $(\gamma ,\lambda H)$. This gives a partial resolution of a conjecture of Bartnik.

Substantial simplification of proof of main theorem. To appear in Class. Quantum Gravity

Cited by in corpus (1)

• Embeddings, immersions and the Bartnik quasi-local mass conjectures