  In this work, radially symmetric kink-like solutions in the presence of
impurities are investigated for both flat and curved $D+1$ spacetimes, with
geometry generated by a rotationally invariant background metric. We have
examined the constraints placed upon the model by Derrick's theorem, and found
out the Bogomol'nyi bound and equations of the symmetric restriction to this
theory. Impurity-doped versions of a $\phi^4$ model in two dimensions and a
model with logarithmic potential in a Schwarzschild background have been
explicitly worked out. The resulting configurations have been compared with
those found in the homogeneous version of the theory, so that the effect of
impurities in the form of solutions may be better appreciated. We have also
generalized to higher dimensions some of the results that had been presented in
the recent literature. These results relate to the possibility of
BPS-preserving impurities, which we have found to still exist in the spacetimes
considered in this work. We also investigate ways in which these results may be
extended in a curved background.
