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
Full-text PDF Free Access
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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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Additional Information
Brian Smith
Affiliation:
University of Alabama at Birmingham, Birmingham, AL 35205
Email:
smith@math.uab.edu
Gilbert Weinstein
Affiliation:
University of Alabama at Birmingham, Birmingham, AL 35205
MR Author ID:
293250
Email:
weinstei@math.uab.edu
Received by editor(s):
May 27, 1999
Published electronically:
July 19, 2000
Additional Notes:
This research was supported in part by NSF grant DMS 9704760.
Communicated by:
Richard Schoen
Article copyright:
© Copyright 2000
American Mathematical Society
