Self-dual two-forms and divergence-free vector fields

Details Self-dual two-forms and divergence-free vector fields Self-dual two-forms and divergence-free vector fields

1997-01-31

arxiv.org/abs/gr-qc/9702001v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, Latex, uses amssym.def amssym.tex and AMS fonts

Scientific paper

Beginning with the self-dual two-forms approach to the Einstein equations, we show how, by choosing basis spinors which are proportional to solutions of the Dirac equation, we may rewrite the vacuum Einstein equations in terms of a set of divergence-free vector fields, which obey a particular set of chiral equations. Upon imposing the Jacobi identity upon these vector fields, we reproduce a previous formulation of the Einstein equations linked with a generalisation of the Yang-Mills equations for a constant connection on flat space. This formulation suggests the investigation of some new aspects of the self-dual two-forms approach. In the case of real Riemannian metrics, these vector fields have a natural interpretation in terms of the torsion of the natural almost-complex-structure on the projective spin-bundle.

Affiliated with

Also associated with

No associations

Rating

Self-dual two-forms and divergence-free vector fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Self-dual two-forms and divergence-free vector fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Self-dual two-forms and divergence-free vector fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-511452