Among the most important reasons for considering the extended theory of Einstein gravity is related to the discovery of the accelerated expansion of our universe, because general relativity provides an insufficient explanation. In this regard, various candidates have been proposed, such as Lovelock gravity, brane world cosmology, scalar–tensor theories, and F(R) gravity. Compact astrophysical objects probe extreme gravitational fields and may be the key to understanding unanswered questions in fundamental physics. The neutron and quark stars, gravastars, and massive white dwarfs are categorized as celestial objects with a high mass and small radius (high density), and, therefore, they are called compact astrophysical objects. Therefore, we must take into account the effects of space–time curvature for investigating their structures. On the other hand, the recent discovery of massive compact objects (such as pulsars, neutron and quark stars, and white dwarfs) contributes to the motivation to study these compact objects in extended theories of gravity, since apparently these massive objects cannot be predicted within general relativity formalism. Potential topics include, but are not limited to, the following: the structure and properties of neutron, quark and boson stars, and (massive) white dwarfs in extended theories of gravity; the properties of gravastars in extended theories of gravity, black hole solutions, and study of the parameters of extended theories of gravity in these solutions.
