12.2 The effective mass of Kulkarni, Chellathurai, and Dadhich for the Kerr spacetime
The Kulkarni-Chellathurai-Dadhich [244] effective mass for the Kerr spacetime is obtained from the
Komar integral (i.e. the linkage with
) using a hypersurface orthogonal vector field
instead of
the Killing vector
of stationarity. The vector field
is defined to be
, where
is
the Killing vector of axi-symmetry and the function
is
. 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
it yields
, while in the limit
it is the
mass parameter
of the solution. The effective mass is computed for the Kerr-Newman spacetime
in [106].