Report on chaos bound outside Taub-NUT black holes

Positions of a charged particle's equilibrium orbits and spatial regions where the chaos bound is violated are found through circular motions of the particle around charged Taub-NUT black holes. Lyapunov exponent is gotten by calculating eigenvalues of a Jacobian matrix in a phase space $(r,\pi_r)$. When the particle's charge is fixed, the positions of the equilibrium orbits gradually move away from the event horizons with the increase of the angular momentum.The result shows that the bound is violated in the near-horizon regions and at a certain distance from the horizons when the charge and NUT parameter are fixed. The spatial regions increase with the increase of the NUT parameter's value.