论文标题
Schwarzschild的外部归纳明显视野的初始数据
Exterior Schwarzschild initial data for degenerate apparent horizons
论文作者
论文摘要
在本说明中，我们表明，如果$ g $是$ \ mathbb {s}^2 $上的平稳的riemannian公制ADM质量任意接近关联的鹰质量$ \ sqrt {\ text {aind {aind}（\ mathbb {s}^2，g）/16π} $。特别是，这确定了Bartnik的准胶质质量（由Bartnik \ cite {Bartnik}在1989年引入）与$（\ Mathbb {s}^2，g）$相关联。我们通过修改Mantoulidis-Schoen \ cite {MS}的构建来证明这些证明，后者在情况下证明了相同的结果$λ_1（l_g）> 0 $。因此，$λ_1（g）\ geq 0 $是必需的，足以满足$（\ mathbb {s}^2，g）$，它来自在显着平坦的时空状态下明显的地平线，在主流能量条件下，并且在时间对称环境中，并且是Bartnik的质量。 $ \ sqrt {\ text {区域}（\ mathbb {s}^2，g）/16π} $。
In this note we show that if $g$ is a smooth Riemannian metric on $\mathbb{S}^2$ such that the first eigenvalue of the operator $L_g:=-Δ_g +K_g$ satisfies $λ_1(L_g)=0$ then $(\mathbb{S}^2, g)$ arises as an apparent horizon in an asymptotically flat initial data set with ADM mass arbitrarily close to the associated Hawking mass $\sqrt{\text{area}(\mathbb{S}^2, g)/16π}$. In particular, this determines the Bartnik quasilocal mass (introduced by Bartnik \cite{Bartnik} in 1989) associated with $(\mathbb{S}^2, g)$ in this setting. We prove these by modifying the construction of Mantoulidis-Schoen \cite{MS} who proved the same results in the case $λ_1(L_g)>0$. It follows that $λ_1(g)\geq 0$ is necessary and sufficient for $(\mathbb{S}^2, g)$ to arise from an apparent horizon in an asyptotically flat space-time under the dominant energy condition and in the time symmetric setting, and that the Bartnik mass of the horizon is $\sqrt{\text{area}(\mathbb{S}^2, g)/16π}$.
