Stellar structure models in modified theories of gravity: lessons and challenges

The understanding of stellar structure represents the crossroads of our theories of the nuclear force and the gravitational interaction under the most extreme conditions observably accessible. It provides a powerful probe of the strong field regime of General Relativity, and opens fruitful avenues for the exploration of new gravitational physics. The latter can be captured via modified theories of gravity, which modify the Einstein-Hilbert action of General Relativity and/or some of its principles. These theories typically change the stellar structure equations, thus having a large impact on the astrophysical properties of the corresponding stars and opening a new window to constrain these theories with present and future observations. For relativistic (neutron) stars, the uncertainty on the equation of state of matter at supranuclear densities intertwines with the new parameters of the modified gravity side, providing new phenomenology for the predictions of stellar structure models, such as mass-radius relations, maximum masses, or moment of inertia. For non-relativistic stars (white, brown and red dwarfs), the weakening/strengthening of the gravitational force inside astrophysical bodies may induce changes on the star's mass, radius or luminosity, having an impact, for instance, in the Chandrasekhar's limit for white dwarfs, or in the minimum mass for stable hydrogen burning in brown dwarfs. This work aims to provide a broad overview of the main such results achieved in the recent literature, by combining the results and constraints obtained from the analysis of relativistic and non-relativistic stars in different scenarios. Moreover, we will build a bridge between the efforts of the community working on different theories, formulations, types of stars, theoretical modellings, and observational aspects, highlighting some of the most promising opportunities in the field.