Generalized Jackiw-Teitelboim gravity in presence of Block brane-like models*

We investigate generalized Jackiw-Teitelboim gravity, coupling the dilaton field with two scalar matter fields. We obtain the equations of motion for the fields and investigate a linear perturbation of the solutions in general. We study two specific situations that allow for analytic solutions with topological behavior and check how the dilaton field, the warp factor and the Ricci scalar behave. In particular, we show how the parameters can be used to modify the structure of the solutions. Moreover, the perturbations are, in general, described by intricate coupled differential equations, but in some specific cases, we can construct the corresponding zero modes analytically.