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arXiv · 2608.08550

Charged Kerr--Levi-Civita geometries in Einstein--Maxwell and low-energy heterotic string theory

Haryanto M. Siahaan
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Abstract

We construct and compare two charged rotating extensions of the Kerr--Levi-Civita geometry. In Einstein--Maxwell theory, a fixed magnetic Kerr--Newman Ernst representative is inverted, and covariance of the coupled Ernst equations, integrability of the dragging and electric-potential quadratures, and the field equations are verified. The resulting local line element agrees with a strong-field representative obtained independently, but no global equivalence of the azimuthal quotients is assumed. In low-energy heterotic string theory, the Hassan--Sen map is instead applied after the vacuum Kerr--Levi-Civita inversion, generating Maxwell, dilaton, and Kalb--Ramond fields. Both branches possess regular local Killing horizons. For the Einstein--Maxwell branch, an exact denominator factorization proves that the subextreme exterior contains neither Ernst zeros nor azimuthal closed timelike curves. The former Kerr ring has finite curvature, although it lies inside an interior region of timelike azimuthal orbits. Its Kretschmann scalar has the form $8\mathcal P_{\rm N}/\mathcal H^6$ and approaches a parameter-independent Levi-Civita law at fixed off-axis latitude. The heterotic branch is qualitatively different: the real component connected to the horizon terminates at a finite-radius $\Lambda=0$ surface. Exact string-frame slice factorizations and independent Einstein-frame calculations show that this surface is a curvature singularity rather than a conformal-frame artifact. Both families are generically Petrov type I. The results distinguish exact local solution generation from the unresolved construction of complete global spacetimes and the identification of possible distributional sources.

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Haryanto M. Siahaan. 2026-08-09. Charged Kerr--Levi-Civita geometries in Einstein--Maxwell and low-energy heterotic string theory. https://arxiv.org/abs/2608.08550

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