Kink collisions in a two-dimensional gravity model

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 possible long-lived resonant excitations in the weak-gravity regime, which may be associated with the persistence of bounce windows. 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.