a Class of Einstein-Maxwell Fields Generalizing the Equilibrium Solutions

Details a Class of Einstein-Maxwell Fields Generalizing the Equilibrium Solutions a Class of Einstein-Maxwell Fields Generalizing the Equilibrium Solutions

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet..939p&link_type=abstract

"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R

Physics

Scientific paper

The Einstein-Maxwell fields of rotating stationary sources are represented by an SU(2,1) spinor potential ΨA satisfying ∇ \cdot [Θ { - 1} (Ψ A ∇ Ψ B - Ψ B ∇ Ψ A )] = - 2Θ { - 2} {C} \cdot {(ψA} ∇ Ψ B - Ψ B ∇ Ψ A ) where Θ = Ψ†. Ψ is the SU(2,1) norm of Ψ. The Ernst potentials are expressed in terms of the spinor potential by ɛ = (Ψ1 - Ψ2)/(Ψ1 + Ψ2), Φ = Ψ3/(Ψ1 + Ψ2). The group invariant vector C = -2iIm{Ψ† · ∇Ψ is generated exclusively by the rotation of the source, hence it is appropriate to refer to C as the swirl of the field. Static fields have no swirl. The fields with no swirl are a class generalizing the equilibrium (|e| = m) class of Einstein-Maxwell fields. We obtain the integrability conditions and a highly symmetrical set of field equations for this class, as well as exact solutions and an open research problem.

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