12.2 The effective mass of Kulkarni, Chellathurai, and Dadhich for the Kerr spacetime

The Kulkarni–Chellathurai–Dadhich [328] effective mass for the Kerr spacetime is obtained from the Komar integral (i.e., the linkage with α = 0) using a hypersurface orthogonal vector field Xa instead of the Killing vector a T of stationarity. The vector field a X is defined to be a a T + ωΦ, where a Φ is the Killing vector of axisymmetry and the function ω is − g(T, Φ)∕g(Φ, Φ ). This is timelike outside the horizon, it is the asymptotic time translation at infinity, and coincides with the null tangent on the event horizon. On the event horizon r = r+ it yields √ -------- MKCD = m2 − a2, while in the limit r → ∞ it is the mass parameter m of the solution. The effective mass is computed for the Kerr–Newman spacetime in [133].
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