K-field kinks in two-dimensional dilaton gravity

TL;DR

This paper investigates kink solutions with non-standard kinetic terms in two-dimensional dilaton gravity, deriving stability criteria and presenting an exact self-gravitating kink solution influenced by a cuscuton term.

Contribution

It introduces a new class of kink solutions with non-canonical kinetic energy in 2D dilaton gravity and provides explicit stability analysis and exact solutions.

Findings

Derived stability criteria for static solutions.

Obtained an exact self-gravitating kink solution.

Analyzed the effects of the cuscuton term.

Abstract

In this work, kinks with non-canonical kinetic energy terms are studied in a type of two-dimensional dilaton gravity model. The linear stability issue is generally discussed for arbitrary static solutions, and the stability criteria are obtained. As an explicit example, a model with cuscuton term is studied. After rewriting the equations of motion into simpler first-order formalism and choosing a polynomial superpotential, an exact self-gravitating kink solution is obtained. The impacts of the cuscuton term are discussed.