On the connectedness of the space of initial data for the einstein equations

Brian Smith; Gilbert Weinstein

doi:10.1090/S1079-6762-00-00081-0

On the connectedness of the space of initial data for the einstein equations

Brian Smith
, Gilbert Weinstein

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

14 Scopus citations

Abstract

Is the space of initial data for the Einstein vacuum equations connected? As a partial answer to this question, we prove the following result: Let M be the space of asymptotically at metrics of non-negative scalar curvature on ℝ³ which admit a global foliation outside a point by 2-spheres of positive mean and Gauss curvatures. Then M is connected.

Original language	English
Pages (from-to)	52-63
Number of pages	12
Journal	Electronic Research Announcements of the American Mathematical Society
Volume	6
Issue number	8
DOIs	https://doi.org/10.1090/S1079-6762-00-00081-0
State	Published - 19 Jul 2000
Externally published	Yes

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abstract = "Is the space of initial data for the Einstein vacuum equations connected? As a partial answer to this question, we prove the following result: Let M be the space of asymptotically at metrics of non-negative scalar curvature on ℝ3 which admit a global foliation outside a point by 2-spheres of positive mean and Gauss curvatures. Then M is connected.",

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AB - Is the space of initial data for the Einstein vacuum equations connected? As a partial answer to this question, we prove the following result: Let M be the space of asymptotically at metrics of non-negative scalar curvature on ℝ3 which admit a global foliation outside a point by 2-spheres of positive mean and Gauss curvatures. Then M is connected.

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On the connectedness of the space of initial data for the einstein equations

Abstract

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