The derivation of Eq. (37
) is not restricted to static configurations. However, when
evaluating the surface terms, one assumes that the horizon is
generated by the same Killing field which is also used in the
dimensional reduction; the asymptotically time-like Killing field
k
. A generalization of the method to rotating black holes requires
the evaluation of the potentials (defined with respect to
k) on a Killing horizon which is generated by
, rather than
k
.