Asymptotically flat extensions of CMC Bartnik data

Abstract

Let $g$ be a metric on the $2$-sphere ${\mathbb{S}}^2$ with positive Gaussian curvature and $H$ be a positive constant. Under suitable conditions on $(g,H)$, we construct smooth, asymptotically flat $3$-manifolds $M$ with non-negative scalar curvature, with outer-minimizing boundary isometric to $({\mathbb{S}}^2,g)$ and having mean curvature $H$, such that near infinity $M$ is isometric to a spatial Schwarzschild manifold whose mass $m$ can be made arbitrarily close to a constant multiple of the Hawking mass of $({\mathbb{S}}^2,g,H)$. Moreover, this constant multiplicative factor depends only on $(g,H)$ and tends to $1$ as $H$ tends to $0$. The result provides a new upper bound of the Bartnik mass associated to such boundary data.

14 pages. v3: updated to agree with published version

References in corpus (1)

• Higher dimensional black hole initial data with prescribed boundary metric

Cited by in corpus (8)

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• Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity