2026/07/24 by Haryanto M. Siahaan
#gr-qc
We construct and analyze stationary, axisymmetric vacuum metrics obtained by magnetic Ernst inversion of Kerr-NUT with Manko-Ruiz parameter C and pre-inversion twist constant β. The transformation lies in the Ehlers orbit; our contribution is the NUT-dependent geometry and the roles of C and β in its axis, horizon, singularity, and azimuthal-CTC structure. The inversion preserves the canonical Weyl radius, the signed WLP numerator F, and the sign of gϕϕ on regular domains. At the selected pole x=σ, C=-σ, the local axis condition and conicity are controlled by χσ(β)=β-2m(2σa+3l). Exterior zeros of the chosen seed Ernst representative obey the exact criterion -β\inRC; for the sampled families numerical traces yield half-line ranges with closed-form corner endpoints. For D=a2+l2-2alC≠0, ΛβΣ has a finite nonzero seed-ring limit. High-precision calculations find direction-independent finite limits of both quadratic Weyl invariants along the sampled rays, without establishing C2-extendibility. At β=0, exterior simple Ernst zeros are found for the sampled C=-1,0 cases but not for C=+1, consistently with the computed ranges. Near one zero the Kretschmann scalar has a generic sixth-order blow-up; a numerical angular scan identifies exceptional directions of lower order. All sampled points in the regular (gϕϕ>0) exterior are Petrov type I. Candidate horizon locations remain those of Kerr-NUT, and the asymptotics are Levi-Civita type.