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- W2954965918 abstract "We construct asymptotically flat, scalar flat extensions of Bartnik data $(Sigma, gamma, H)$, where $gamma$ is a metric of positive Gauss curvature on a two-sphere $Sigma$, and $H$ is a function that is either positive or identically zero on $Sigma$, such that the mass of the extension can be made arbitrarily close to the half area radius of $(Sigma, gamma)$. In the case of $H equiv 0$, the result gives an analogue of a theorem of Mantoulidis and Schoen, but with extensions that have vanishing scalar curvature. In the context of initial data sets in general relativity, the result produces asymptotically flat, time-symmetric, vacuum initial data with an apparent horizon $(Sigma, gamma)$, for any metric $gamma$ with positive Gauss curvature, such that the mass of the initial data is arbitrarily close to the optimal value in the Riemannian Penrose inequality. The method we use is the Shi-Tam type metric construction from cite{ShiTam02} and a refined Shi-Tam monotonicity, found by the first named author in cite{Miao09}." @default.
- W2954965918 created "2019-07-12" @default.
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- W2954965918 date "2019-07-03" @default.
- W2954965918 modified "2023-09-26" @default.
- W2954965918 title "Bartnik mass via vacuum extensions" @default.
- W2954965918 cites W1498143011 @default.
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- W2954965918 doi "https://doi.org/10.48550/arxiv.1907.02039" @default.
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