Bianchi and Weyl equations as sufficient equations for Einstein spaces |
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Authors: | S Brian Edgar |
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Institution: | (1) Department of Mathematics, University of Linköping, S-581 83 Linköping, Sweden |
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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-spinor
ABCD
considered arbitrary and with the background space unspecified,
EA
EBCD=0; ( +12 )
ABCD
–6 (AB
EF
(
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-spinor
ABCD
has to be the Weyl spinor of this space. |
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Keywords: | |
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