Revisit on two-dimensional self-gravitating kinks: superpotential formalism and linear stability

TL;DR

This paper revisits two-dimensional self-gravitating kink solutions, deriving analytical solutions via superpotential formalism and establishing their linear stability through a Schrödinger-like analysis.

Contribution

It introduces a superpotential approach to derive analytical kink solutions and provides a general linear stability analysis for these solutions in two-dimensional dilaton gravity.

Findings

Analytical kink solutions derived from superpotential formalism.

Linear stability confirmed via Schrödinger-like equation with factorizable Hamiltonian.

General stability analysis applicable to arbitrary static solutions.

Abstract

Self-gravitating kink solutions of a two-dimensional dilaton gravity are revisited in this work. Analytical kink solutions are derived from a concise superpotential formalism of the dynamical equations. A general analysis on the linear stability is conducted for an arbitrary static solution of the model. After gauge fixing, a Schr\"odinger-like equation with factorizable Hamiltonian operator is obtained, which ensures the linear stability of the solution.