Perturbed Self-Similar Massless Scalar Field in the Spacetimes with Circular Symmetry in 2+1 Gravity

TL;DR

This paper analyzes linear perturbations of a 2+1-dimensional circularly symmetric scalar field spacetime, demonstrating the background solution's stability through exact solutions of perturbation equations.

Contribution

It provides the first exact solutions for perturbation modes of this specific self-similar spacetime in 2+1 gravity, confirming its stability.

Findings

Background solution is stable under linear perturbations.

Exact solutions for perturbation equations were obtained.

The study advances understanding of scalar field dynamics in lower-dimensional gravity.

Abstract

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.