Alpha Surfaces for Complex Space-Times with Torsion

Details Alpha Surfaces for Complex Space-Times with Torsion Alpha Surfaces for Complex Space-Times with Torsion

1995-07-01

arxiv.org/abs/gr-qc/9506090v1

NuovoCim.B108:123-126,1993

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, plain-tex, published in Nuovo Cimento B, volume 108, pages 123-125, year 1993

Scientific paper

10.1007/BF02874404

This paper studies necessary conditions for the existence of alpha-surfaces in complex space-time manifolds with nonvanishing torsion. For these manifolds, Lie brackets of vector fields and spinor Ricci identities contain explicitly the effects of torsion. This leads to an integrability condition for alpha-surfaces which does not involve just the self-dual Weyl spinor, as in complex general relativity, but also the torsion spinor, in a nonlinear way, and its covariant derivative. Interestingly, a particular solution of the integrability condition is given by conformally right-flat and right-torsion-free space-times.

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