The Asymptotically Self-Similar Regime for the Einstein Vacuum Equations

Igor Rodnianski; Yakov Shlapentokh-Rothman

doi:10.1007/s00039-018-0448-9

The Asymptotically Self-Similar Regime for the Einstein Vacuum Equations

Igor Rodnianski, Yakov Shlapentokh-Rothman

Mathematics

Princeton University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify exact self-similar solutions which correspond to the formal asymptotic expansions of Fefferman–Graham’s ambient metric.

Original language	American English
Pages (from-to)	755-878
Number of pages	124
Journal	Geometric and Functional Analysis
Volume	28
Issue number	3
DOIs	https://doi.org/10.1007/s00039-018-0448-9
State	Published - Jun 1 2018

ASJC Scopus subject areas

Analysis
Geometry and Topology

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Cite this

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title = "The Asymptotically Self-Similar Regime for the Einstein Vacuum Equations",

abstract = "We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify exact self-similar solutions which correspond to the formal asymptotic expansions of Fefferman–Graham{\textquoteright}s ambient metric.",

author = "Igor Rodnianski and Yakov Shlapentokh-Rothman",

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N2 - We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify exact self-similar solutions which correspond to the formal asymptotic expansions of Fefferman–Graham’s ambient metric.

AB - We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify exact self-similar solutions which correspond to the formal asymptotic expansions of Fefferman–Graham’s ambient metric.

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The Asymptotically Self-Similar Regime for the Einstein Vacuum Equations

Abstract

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