Abstract
The relativistic field equations of the axistationary vacuum are derived in Ernst coordinates in full detail. The derivation of the Kerr metric is given from the field equations.
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The class of fields for which the functions α and γ are analytic has been noted by D. Kramer. It can be shown that α,=2γ,1=0 alone suffice to characterize the Kerr metric
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Kadlecsik, J. New approaches to the axisymmetric vacuum. Z. Phys. C - Particles and Fields 41, 265–269 (1988). https://doi.org/10.1007/BF01566925
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DOI: https://doi.org/10.1007/BF01566925