Singular P\"oschl-Teller II potentials and gravitating kinks

TL;DR

This paper introduces an exactly solvable 2D gravitating kink model with a sine-Gordon background, analyzing its stability and vibrational modes through a Schrödinger-like equation with singular P"oschl-Teller II potentials.

Contribution

It presents a novel 2D gravitating kink model with exact solutions and stability analysis, including the spectrum of vibrational modes, advancing understanding of thick brane world solutions.

Findings

No tachyonic states, ensuring stability.

Existence of multiple bounded vibrational modes.

Spectrum depends on model parameters.

Abstract

We report a two-dimensional (2D) gravitating kink model, for which both the background field equations and the linear perturbation equation are exactly solvable. The background solution describes a sine-Gordon kink that interpolating between two asymptotic AdS$_2$ spaces, and can be regarded as a 2D thick brane world solution. The linear perturbation equation can be recasted into a Schr\"odinger-like equation with singular P\"oschl-Teller II potentials. There is no tachyonic state in the spectrum, so the solution is stable against the linear perturbations. Besides, there can be $n=0,1,2,\cdots$ bounded vibrational modes around the kink. The number of these vibrational modes varies with model parameters.