Communications in Mathematical Physics

, Volume 32, Issue 4, pp 291–304

Instability of closed spaces in general relativity

  • Dieter R. Brill
  • Stanley Deser

DOI: 10.1007/BF01645610

Cite this article as:
Brill, D.R. & Deser, S. Commun.Math. Phys. (1973) 32: 291. doi:10.1007/BF01645610


There are strong restrictions on the solutions of the initial value constraints of General Relativity when the spatial hypersurface is closed. In particular, closed flat space is unstable: not all solutions of the linearized constraints correspond to nearby solutions of the constraints themselves. For example, no nearby solutions whatever exist which are time symmetric. Other restrictions, which limit perturbations of non-flat closed initial solutions, are also exhibited.

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Dieter R. Brill
    • 1
    • 2
  • Stanley Deser
    • 3
    • 4
  1. 1.Max Planck Institute for Physics and AstrophysicsMunichGermany
  2. 2.Department of Physics and AstronomyUniversity of MarylandCollege ParkUSA
  3. 3.Laboratoire de Physique Théorique et Hautes EnergiesOrsayFrance
  4. 4.Physics DepartmentBrandeis UniversityWalthamUSA

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