On the Topology of Vacuum Spacetimes
Abstract.We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n + 1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary compact manifold \( \Sigma^n \) to an asymptotically Euclidean solution of the constraints on \( \mathbb{R}^n \). For any \( \Sigma^n \) which does not admit a metric of positive scalar curvature, this provides for the existence of asymptotically flat vacuum spacetimes with no maximal slices. Our main theorem is a special case of a more general gluing construction for nondegenerate solutions of the vacuum constraint equations which have some restrictions on the mean curvature, but for which the mean curvature is not necessarily constant. This generalizes the construction [16], which is restricted to constant mean curvature data.
Similar content being viewed by others Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. Author information Authors and AffiliationsUniversity of Oregon, Department of Mathematics, Eugene, OR 97403-1221, USA, e-mail: jim@newton.uoregon.edu, USA
J. Isenberg
Stanford University, Department of Mathematics, Stanford, CA 94305, USA, e-mail: mazzeo@math.stanford.edu, USA
R. Mazzeo
University of Washington, Mathematics Department, Box 354350, Seattle, WA 98195-4350, USA, e-mail: pollack@math.washington.edu, USA
D. Pollack
Submitted 11/07/02, accepted 15/11/02
RID="*"
ID="*"Communicated by Piotr Chrusciel and Sergiu Klainerman
About this article Cite this articleIsenberg, J., Mazzeo, R. & Pollack, D. On the Topology of Vacuum Spacetimes . Ann. Henri Poincaré 4, 369–383 (2003). https://doi.org/10.1007/s00023-003-0133-9
Published: 01 March 2003
Issue Date: March 2003
DOI: https://doi.org/10.1007/s00023-003-0133-9
RetroSearch is an open source project built by @garambo | Open a GitHub Issue
Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo
HTML:
3.2
| Encoding:
UTF-8
| Version:
0.7.4