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arXiv · 2308.13031

Initial data gluing in the asymptotically flat regime via solution operators with prescribed support properties

Yuchen Mao·Sung-Jin Oh·Zhongkai Tao
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Abstract

We give new proofs of general relativistic initial data gluing results on unit-scale annuli based on explicit solution operators for the linearized constraint equation around the flat case with prescribed support properties. These results retrieve and optimize - in terms of positivity, regularity, size and/or spatial decay requirements - a number of known theorems concerning asymptotically flat initial data, including Kerr exterior gluing by Corvino-Schoen and Chru\'sciel-Delay, interior gluing (or "fill-in") by Bieri-Chru\'sciel, and obstruction-free gluing by Czimek-Rodnianski. In particular, our proof of the strengthened obstruction-free gluing theorem relies on purely spacelike techniques, rather than null gluing as in the original approach.

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Yuchen Mao, Sung-Jin Oh, Zhongkai Tao. 2023-08-24. Initial data gluing in the asymptotically flat regime via solution operators with prescribed support properties. https://arxiv.org/abs/2308.13031

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