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arXiv · 2210.09437

Localized initial data for Einstein equations

Yuchen Mao·Zhongkai Tao
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Abstract

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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Yuchen Mao, Zhongkai Tao. 2022-10-17. Localized initial data for Einstein equations. https://arxiv.org/abs/2210.09437

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