Taub-NUT solutions in conformal electrodynamics

TL;DR

This paper presents a new charged Taub-NUT spacetime solution within the conformally invariant ModMax electrodynamics, highlighting its unique magnetic field features and thermodynamic properties, expanding the landscape of non-linear electrodynamics solutions.

Contribution

It provides the first non-trivial self-gravitating solution in the ModMax theory, demonstrating the effects of non-linearity and duality invariance on Taub-NUT spacetimes.

Findings

The solution exhibits non-trivial magnetic fields due to non-linearity.

Thermodynamics of the solution is analyzed, including black hole limits.

Self-dual solutions are also discussed.

Abstract

We construct a novel charged Taub-NUT spacetime, providing a first non-trivial example of a self-gravitating solution to the recently proposed ModMax theory, the most general (1-parametric) theory of non-linear electrodynamics that is characterized by both the conformal symmetry and the $SO(2)$ duality-rotation invariance. The spacetime features non-trivial magnetic fields, in their presence the non-linearity of the field becomes apparent and the solution is distinguished from that of the Maxwell theory. Thermodynamics of the new solution, the charged black hole limit of vanishing NUT parameter, and the self-dual solutions are also briefly discussed.