  The kink stability of self-similar solutions of a massless scalar field with
circular symmetry in 2+1 gravity is studied, and found that such solutions are
unstable against the kink perturbations along the sonic line (self-similar
horizon). However, when perturbations outside the sonic line are considered,
and taking the ones along the sonic line as their boundary conditions, we find
that non-trivial perturbations do not exist. In other words, the consideration
of perturbations outside the sonic line limits the unstable mode of the
perturbations found along the sonic line. As a result, the critical solution
for the scalar collapse remains critical even after the kink perturbations are
taken into account.
