Singular Pöschl-Teller II potentials and gravitating kinks

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 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 $n=0,1,2,\cdots$ bounded vibrational modes around the kink. The number of these vibrational modes varies with model parameters.

13 pages, 2 figures. Minor revision of the text, Fig. 2 is redrawn, and some new references are added

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