Consistent mass formulas for the four-dimensional dyonic NUT-charged spacetimes

In our previous work, a novel idea that the NUT charge can be thought of as thermodynamical multi-hair has been advocated to describe perfectly character generic four-dimensional Taub-NUT spacetimes. According this scheme, Komar mass M, gravito-magnetic and/or dual (magnetic) N, together with new secondary hair J_N=MN, namely, Kerr-like conserved angular momentum, enter into standard forms first law and Bekenstein-Smarr formula. Distinguished from other recent attempts, consistent thermodynamic differential integral formulae are both obtainable meaningful Christodoulou-Ruffini-type squared formula almost all NUT-charged As an excellent consequence, famous Bekenstein-Hawking one-quarter area-entropy relation naturally restored not only in Lorentzian sector but also Euclidian counterpart Taub-NUT-type spacetimes without imposing any constraint condition. However, purely electric-charged cases Einstein-Maxwell gravity theory have addressed there. paper, we shall follow simple, systematic way proposed article further investigate dyonic case. It is shown relations continue hold true provided no added, however, so-obtained electrostatic magneto-static potentials coincident those computed via method. To rectify inconsistence, simple strategy by introducing two additional hairs: Q_N=QN P_N=PN, their conjugate potentials, so still satisfied.