2000/03/28 by Zoltán Perjés, Perjés, Zoltán
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.gr-qc/0003102
openalex publication_date 2000/03/28 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The Einstein-Maxwell fields of rotating stationary sources are represented by\nthe SU(2,1) spinor potential \ΨA satisfying \
nabla
cdot [
Theta\n-1(
PsiA
nabla
PsiB-
PsiB
nabla
PsiA)]=-2
Theta -2
vecC
cdot\n(
PsiA
nabla
PsiB-
PsiB
nabla
PsiA) where \Θ =\Ψ \†\n\⋅ \Ψ is the SU(2,1) norm of \Ψ % . The Ernst potentials are\nexpressed in terms of the spinor potential by % cal E=\(\Ψ1-\Ψ\n2)/(\Ψ1+\Ψ2), \Φ =\(\Ψ3)/(% \Ψ1+\Ψ2) . The group\ninvariant vector \C=-2i funcIm \Ψ \†\⋅ \∇ \Ψ is\ngenerated exclusively by the rotation of the source, hence it is appropriate to\nrefer to \C as the em swirl of the field. Static fields have no\nswirl.\n The fields with no swirl are a class generalizing the equilibrium (| e| =m)\nclass of Einstein-Maxwell fields. We obtain the integrability conditions and a\nhighly symmetrical set of field equations for this class, as well as exact\nsolutions and an open research problem.\n