First law for Kerr Taub-NUT AdS black holes

A bstract The first law of black hole mechanics, which relates the change energy to entropy and other conserved charges, has been main motivation for probing thermodynamic properties holes. In this work, we investigate thermodynamics Kerr Taub-NUT AdS We present geometric Komar definitions that by construction satisfy Smarr formula. Further, a scaling argument based on Euler’s theorem, establish corresponding includes variations in cosmological constant, NUT charges angular momenta. key new ingredient are independent both momenta, Misner string Employing Brown-York quasi-local charge show our expression mass spin coincide with generalized expressions. indicate relevance these results rotating holes, including proper choice time-like Killing vector produce correct mass.