Kink collisions in a two-dimensional gravity model

Abstract

We numerically study kink-antikink collisions in the self-gravitating $\phi^4$ model coupled to the two-dimensional dilaton gravity theory proposed by Mann et al. The static kink solutions interpolate between an anti-de Sitter (AdS$_2$) region and a Minkowski region, and can be regarded as two-dimensional analogues of certain thick branes. By scanning the initial velocity for several gravitational couplings, we find that gravity modifies the scattering structure: the resonance windows shift toward higher initial velocities and become progressively narrower as the coupling $\kappa$ increases, while the critical escape velocity increases mildly. A linear perturbation analysis further indicates that the shape modes turn into long-lived quasi-bound states in the weak-gravity regime, which could leak energy during collisions and may therefore contribute to the shift and narrowing of the windows and the increase of the critical velocity. The collisions further produce a clear geometrical response: the conformal factor decreases after the collision, corresponding to a contraction of the local proper spatial scale in the conformal gauge, and this effect becomes stronger for larger $\kappa$. Meanwhile, the Ricci scalar develops transient peaks during kink encounters but remains finite in all simulations considered. Thus, in contrast to higher-dimensional thick-brane collisions, we find no evidence for spacetime singularity formation in this two-dimensional model.