  In this work we address a way to capture scalar field solutions on static
spacetimes by using BPS formalism and relaxing the general covariance
condition. We focus on configurations where the background geometry describes
topological black holes and present both analytical and numerical solutions, in
addition to discussing the use of conserved charges associated to such field
configurations. The obtained solutions are radially stable and the zero-mode
arising from the stability equation can be written analytically.
