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

Smith, Brian; Weinstein, Gilbert

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

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

Authors: Brian Smith and Gilbert Weinstein
Journal: Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 52-63
MSC (2000): Primary 83C05; Secondary 58G11
DOI: https://doi.org/10.1090/S1079-6762-00-00081-0
Published electronically: July 19, 2000
MathSciNet review: 1777856
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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 $\mathcal {M}$ be the space of asymptotically flat metrics of non-negative scalar curvature on $\mathbb {R}^3$ which admit a global foliation outside a point by $2$-spheres of positive mean and Gauss curvatures. Then $\mathcal {M}$ is connected.

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