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General Relativity and Gravitation

, Volume 27, Issue 2, pp 223–231 | Cite as

Bianchi and Weyl equations as sufficient equations for Einstein spaces

  • S. Brian Edgar
Article

Abstract

When the Bianchi equation and the wave equation for the Weyl spinor are written in the form which they take for Einstein spaces, but with the symmetric 4-spinorΦ ABCD considered arbitrary and with the background space unspecified, ∇ EA′ ΦEBCD=0; (□+12λ)Φ ABCD −6Φ(AB EF (Φ CD )EF =0 it is shown that — in general — for this pair of equations to be consistent, the background space has to be an Einstein space, and the symmetric 4-spinorΦ ABCD has to be the Weyl spinor of this space.

Keywords

Wave Equation Differential Geometry Einstein Space Weyl Spinor Background Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • S. Brian Edgar
    • 1
  1. 1.Department of MathematicsUniversity of LinköpingLinköpingSweden

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