The Off-shell ADT Charges Of Rotating Black Holes In Einstein Gravity

In the framework of Einstein gravity,we apply the Abbort-Deser-Tekin(ADT)formalism and its off-shell generalization(off-shell ADT)to explore the mass and angular momentum of rotating black holes.First,we utilize the ADT method to compute the mass and angular momentum of the three-dimensional(3D)BTZ black hole and the 4D Kerr black hole.By comparison,the off-shell ADT method is also applied to them.All the results agree with each other.Second,as a further extension of the 4D case,we calculate the off-shell ADT mass and two angular momentums of the 5D Myers-Perry black holes.For these black holes,the off-shell ADT charges satisfy the differential and integral forms of the first law of black hole thermodynamics,which are also consistent with the results in terms of the Komar formula and the ADM formalism.Finally,the off-shell ADT method is extended to the asymptotically rotating Kerr-AdS black holes in arbitrary dimensions.It is demonstrated that the asymptotically rotating effect may make the mass non-integrable when the asymptotic non-rotating timelike Killing vector associated with the mass is allowed to vary and the fluctuation of the metric is determined by the variation of all the mass and rotation parameters.To obtain a physically meaningful mass,it is proposed that one can let the non-rotating timelike Killing vector be fixed or directly perform calculations in the asymptotically static frame.This results further support that the ADT formalism is background dependent.