Perturbed Self-Similar Massless Scalar Field in the Spacetimes with   Circular Symmetry in 2+1 Gravity
  We present in this work the study of the linear perturbations of the 2+1-dimensional circularly symmetric solution, obtained in a previous work, with kinematic self-similarity of the second kind. We have obtained an exact solution for the perturbation equations and the possible perturbation modes. We have shown that the background solution is a stable solution. 
R. Chan, M. F. A. da Silva, Jaime F. Villas da Rocha