Singular Pöschl-Teller II potentials and gravitating kinks
arXiv:2207.12681 · doi:10.1007/JHEP09(2022)165
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 spaces, and can be regarded as a 2D thick brane world solution. The linear perturbation equation can be recasted into a Schrödinger-like equation with singular Pöschl-Teller II potentials. There is no tachyonic state in the spectrum, so the solution is stable against the linear perturbations. Besides, there can be bounded vibrational modes around the kink. The number of these vibrational modes varies with model parameters.
arXiv comment13 pages, 2 figures. Minor revision of the text, Fig. 2 is redrawn, and some new references are added
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