OP is apparently looking for 1D structures:
On one hand, a 3+1D Kerr black hole has a 1D ring singularity.
On the other hand, an event horizon has always codimension 1 in spacetime. In 3+1D we speak of the event-horizon as a 2D area, i.e. we are implicitly suppressing 1 dimension. According to that terminology the event-horizon becomes a 1D length in 2+1D.