Generalized Einstein-ModMax-ScalarField theories and new exact solutions

TL;DR

This paper develops a generalized framework for stationary, axisymmetric spacetimes with scalar and electrodynamic fields, deriving new exact rotating solutions relevant for ModMax and related theories.

Contribution

It introduces a broad Ernst-type approach that includes nonzero rotation and scalar couplings, leading to two novel families of exact solutions in nonlinear electrodynamics.

Findings

Derived two new exact rotating solutions in ModMax-like theories.

Framework accommodates diverse scalar couplings including dilatonic and phantom sectors.

Solutions preserve nonlinear features of ModMax while allowing analytical treatment.

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.