Consistent mass formulas for higher even-dimensional Reissner-Nordström-NUT-AdS spacetimes

In our previous work [D. Wu and S.-Q. Wu, Phys. Rev. D 108, 064034 (2023)], we have formulated consistent thermodynamic first law and Bekenstein-Smarr mass formulae for all higher even-dimensional uncharged Taub-NUT (AdS) spacetimes through the inclusion of a secondary hair $J_n=Mn$ as did in the four-dimensional NUT-charged cases [S.-Q. Wu and D. Wu, Phys. Rev. D 100, 101501® (2019)]. In this article, we will show that the corresponding Reissner-Nordström(RN)-NUT (AdS) cases in all higher even-dimensions can be coherently treated just like the uncharged cases if another secondary hair $Q_n\propto qn$ is further introduced as did in the four-dimensional dyonic NUT-charged case [D. Wu and S.-Q. Wu, Phys. Rev. D 105, 124013 (2022)]. As a by-product of our consequence, it is also demonstrated that there is no need to introduce the secondary hair $Q_n$ in the mass formulae for the four-dimensional purely electric-charged RN-NUT (AdS) spacetimes.