  In the main article [CQG 38 (2021) 055003], a new "canonical" form for the
Lewis metrics of the Weyl class has been obtained, depending only on three
parameters -- Komar mass and angular momentum per unit length, plus the angle
deficit -- corresponding to a coordinate system fixed to the "distant stars"
and an everywhere timelike Killing vector field. Such form evinces the local
but non-global static character of the spacetime, and striking parallelisms
with the electromagnetic analogue. We discuss here its generality, main
physical features and important limits (the Levi-Civita static cylinder, and
spinning cosmic strings). We contrast it on geometric and physical grounds with
the Kerr spacetime -- as an example of a metric which is locally non-static.
