A more direct representation for complex relativity

Details A more direct representation for complex relativity A more direct representation for complex relativity

2007-07-31

arxiv.org/abs/0707.4681v1

AnnalenPhys.16:615-639,1997

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages

Scientific paper

10.1002/andp.200610250

An alternative to the representation of complex relativity by self-dual complex 2-forms on the spacetime manifold is presented by assuming that that the bundle of real 2-forms is given an almost-complex structure. From this, one can define a complex orthogonal structure on the bundle of 2-forms, which results in a more direct representation of the complex orthogonal group in three complex dimensions. The geometrical foundations of general relativity are then presented in terms of the bundle of oriented complex orthogonal 3-frames on the bundle of 2-forms in a manner that essentially parallels their construction in terms of self-dual complex 2-forms. It is shown that one can still discuss the Debever-Penrose classification of the Riemannian curvature tensor in terms of the representation presented here.

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