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arxiv: 2210.09437 · v2 · pith:ZTRSM6RSnew · submitted 2022-10-17 · 🧮 math.AP · math.DG

Localized initial data for Einstein equations

Yuchen Mao , Zhongkai Tao This is my paper
classification 🧮 math.AP math.DG
keywords datainitialalphaasymptoticallyeinsteinflatapplicationsapply
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We apply a new method with explicit solution operators to construct asymptotically flat initial data sets of the vacuum Einstein equation with new localization properties. Applications include an improvement of the decay rate in Carlotto--Schoen [arXiv:1407.4766] to $\mathcal{O}(|x|^{-(d-2)})$ and a construction of nontrivial asymptotically flat initial data supported in a degenerate sector $\{(x',x_d)\in\mathbb{R}^d:|x'|\leq x_d^\alpha\}$ for $\frac{3}{d+1}<\alpha<1$.

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