Normal modes for two-dimensional gravitating kinks

TL;DR

This paper analyzes small perturbations around static kink solutions in a 2D gravity-scalar system, deriving normal mode equations and providing a Mathematica code for the calculations.

Contribution

It introduces a systematic method to derive the quadratic action and normal modes for perturbations in a 2D gravity-scalar kink system, including gauge fixing and constraint handling.

Findings

Derived the quadratic action for perturbations around 2D gravitating kinks.

Confirmed the linear perturbation equations match those from linearized field equations.

Provided computational tools to facilitate similar analyses.

Abstract

We study small perturbations around an arbitrary static kink solution of a two-dimensional (2D) gravity-scalar system, where the gravity part is described by a subclass of 2D dilaton gravity theory, and the scalar matter field has generalized dynamics. We expand the action around an arbitrary static solution and keep terms up to the second order of the perturbations. After variation the linear-order action leads to background field equations, as expected. The quadratic action of the normal modes are obtained after fixing the gauge and using the constraint equation. The linear perturbation equations obtained from the quadratic action are consistent with those obtained by linearizing the field equations under the dilaton gauge. All the calculations are assisted by a Mathematica code, which is also provided as a supplementary material.