On the NUT-Born-Infeld-$\mathrm{\Lambda }$ spacetime

The stationary axisymmetric spacetime coupled to nonlinear Born-Infeld electrodynamics is studied. The solution was derived by Plebanski et al (1984) and it is characterized by six free parameters: mass, NUT charge, electric and magnetic charge, Born-Infeld parameter and cosmological constant. The geodesic and Lorentz force equations are integrated, and a qualitative analysis of the effect of varying the parameters in the effective potential is provided. Then the light and charged particle trajectories are discussed. The conditions that determine an extreme black hole are presented as well.