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arXiv · 2603.26073

Generalized Einstein-ModMax-ScalarField theories and new exact solutions

Leonel Bixano·Tonatiuh Matos
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Abstract

We present a generalized Ernst-type framework for stationary, axisymmetric spacetimes in which a scalar field is coupled to the electrodynamic field, with a particular focus on the ModMax theory. Our approach relies on the Weyl stationary-axisymmetric ansatz and explicitly allows for a nonzero rotational metric function, $\omega\neq 0$. The resulting setup is broad enough to encompass wide classes of scalar couplings, including dilatonic and phantom-like sectors, and can be tailored to specific models such as Einstein-ModMax, Kaluza-Klein theories, low-energy string-inspired scenarios, entanglement relativity and related generalizations. Within this scheme, we derive two novel families of exact rotating solutions in the sector where the electromagnetic invariants obey $\mathcal F/\mathcal G=\mathrm{constant}$. This regime is particularly significant for ModMax, as it preserves genuinely nonlinear features while still admitting an analytically manageable description.

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Leonel Bixano, Tonatiuh Matos. 2026-03-27. Generalized Einstein-ModMax-ScalarField theories and new exact solutions. https://arxiv.org/abs/2603.26073

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