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In several classes of modified gravity theories, extra degrees of freedom arenot completely screened in the interiors of stellar and substellar objects. Insuch theories, the hydrostatic equilibrium condition inside these objects isaltered. Moreover, the interior structures of these objects might have a smallpressure anisotropy induced by several physical phenomena, including rotationand magnetic fields. All these effects, both individually and collectively,induce changes in predicted stellar observables. Such changes have an impact ondifferent phases of the stellar life cycle, starting from its birth to itsdeath, covering almost all the branches of the Hertzsprung-Russell diagram. Theaim of this work is to systematically review the current literature on thetopic. We discuss the main results and constraints obtained on a class ofmodified gravity theories.

Anisotropies and modified gravity theories in stellar and substellar objects