On Stationary Vacuum Solutions to the Einstein Equations

  title={On Stationary Vacuum Solutions to the Einstein Equations},
  author={Michael T. Anderson},
A stationary space-time (M,g) is a 4-manifold M with a smooth Lorentzian metric g, of signature (−,+,+,+), which has a smooth 1-parameter group G ≈ R of isometries whose orbits are time-like curves in M . We assume throughout the paper that M is a chronological space-time, i.e. M admits no closed time-like curves, c.f. §1.1 for further discussion. Let S be the orbit space of the action G. Then S is a smooth 3-manifold, (Hausdorff and paracompact), for which the projection 

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Publications referenced by this paper.

Scalar curvature, metric degenerations and the static vacuum Einstein equations on 3manifolds I

  • M. Anderson
  • Geom. and Funct. Anal.,
  • 1999

On the structure of solutions to the static vacuum Einstein equations, (preprint, S.U.N.Y

  • M. Anderson
  • Stony Brook, July
  • 1998

Conformally stationary space-times, Class

  • S. Harris
  • Quantum Gravity,
  • 1992

A report on harmonic maps , Bull

  • L. Lemaire
  • London Math . Soc .
  • 1990

A convergence theorem for Riemannian manifolds and some applications

  • A. Kasue
  • Nagoya Math. J.,
  • 1989

General Relativity

  • R. Wald
  • 1984

Essential Relativity, 2 Edition

  • W. Rindler
  • 1977

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