Localized initial data for Einstein equations

2022/10/17 by Mao, Yuchen, Tao, Zhongkai
#35Q76 #83C05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.09437

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 O(|x|^-(d-2)) and a construction of nontrivial asymptotically flat initial data supported in a degenerate sector \(x',x_d)∈ℝ^d:|x'|≤ x_d^α\ for (3)/(d+1)<α<1.

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