Bianchi and Weyl equations as sufficient equations for Einstein spaces

Details Bianchi and Weyl equations as sufficient equations for Einstein spaces Bianchi and Weyl equations as sufficient equations for Einstein spaces

Feb 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995gregr..27..223e&link_type=abstract

General Relativity and Gravitation, Volume 27, Issue 2, pp.223-231

Physics

Scientific paper

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.

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