  In a stationary axisymmetric spacetime, the angular velocity of a stationary
observer that Fermi-Walker transports its acceleration vector is also the
angular velocity that locally extremizes the magnitude of the acceleration of
such an observer, and conversely if the spacetime is also symmetric under
reversing both t and phi together. Thus a congruence of Nonrotating
Acceleration Worldlines (NAW) is equivalent to a Stationary Congruence
Accelerating Locally Extremely (SCALE). These congruences are defined
completely locally, unlike the case of Zero Angular Momentum Observers (ZAMOs),
which requires knowledge around a symmetry axis. The SCALE subcase of a
Stationary Congruence Accelerating Maximally (SCAM) is made up of stationary
worldlines that may be considered to be locally most nearly at rest in a
stationary axisymmetric gravitational field. Formulas for the angular velocity
and other properties of the SCALEs are given explicitly on a generalization of
an equatorial plane, infinitesimally near a symmetry axis, and in a slowly
rotating gravitational field, including the weak-field limit, where the SCAM is
shown to be counter-rotating relative to infinity. These formulas are evaluated
in particular detail for the Kerr-Newman metric. Various other congruences are
also defined, such as a Stationary Congruence Rotating at Minimum (SCRAM), and
Stationary Worldlines Accelerating Radially Maximally (SWARM), both of which
coincide with a SCAM on an equatorial plane of reflection symmetry.
Applications are also made to the gravitational fields of maximally rotating
stars, the Sun, and the Solar System.
