Are black holes in an ekpyrotic phase possible?

The ekpyrotic phase (a slow contraction cosmic phase before the current expansion phase) manages to solve the main problems of the standard cosmology by means of a scalar field interpreted as a cosmic fluid in the Friedmann equation. Moreover, this phase generates a nearly scale-invariant spectrum of perturbations in agreement with the latest data. Then, the ekpyrotic mechanism is a serious possibility to the inflationary model. In this work, by using the approach of deforming metrics at linear level, we point out that it is impossible to generate a black hole with spherical symmetry supported by an isotropic fluid in this cosmological scenario.