Exact rotating dilatonic branch in ModMax electrodynamics without Maxwell analogue

TL;DR

This paper introduces a new class of exact rotating dilatonic solutions in Einstein-ModMax gravity, which are inherently nonlinear and include black-hole configurations with physically acceptable exterior regions.

Contribution

It presents the first exact rotating dilatonic solutions in ModMax electrodynamics that lack Maxwell analogs, including black-hole solutions with well-behaved exteriors.

Findings

Solution is intrinsically tied to nonlinear ModMax regime.

Includes both NUT and asymptotically flat solutions.

Identifies a black-hole regime with a hidden singularity.

Abstract

We present a novel class of rotating dilatonic solutions within the framework of Einstein-ModMax-type gravity. The configuration belongs to the nonlinear sector characterized by $\mathcal F/\mathcal G=\mathrm{const}$ and carries nontrivial electric and magnetic potentials, with both $A_t$ and $A_\varphi$ turned on, together with a nontrivial gravitomagnetic structure. We show that this solution does not admit continuation to the Maxwell framework of our parametrization, so it is intrinsically tied to the nonlinear ModMax regime. It includes both a NUT geometry and a NUT-free asymptotically flat limit, and it is valid for a broad class of dilatonic couplings, including the low-energy string and Kaluza-Klein cases. Moreover, in the prolate sector we identify a genuine black-hole regime in which the exterior region satisfies the null energy condition while the curvature singularity remains hidden behind the event horizon. These results provide an exact rotating dilatonic ModMax configuration with no Maxwell analog and a physically well-behaved exterior black-hole sector.