Anisotropies and modified gravity theories in stellar and substellar objects

In several classes of modified gravity theories, extra degrees of freedom are not completely screened in the interiors of stellar and substellar objects. In such theories, the hydrostatic equilibrium condition inside these objects is altered. Moreover, the interior structures of these objects might have a small pressure anisotropy induced by several physical phenomena, including rotation and magnetic fields. All these effects, both individually and collectively, induce changes in predicted stellar observables. Such changes have an impact on different phases of the stellar life cycle, starting from its birth to its death, covering almost all the branches of the Hertzsprung-Russell diagram. The aim of this work is to systematically review the current literature on the topic. We discuss the main results and constraints obtained on a class of modified gravity theories.