We consider a system of interacting spinor and scalar fields in a gravitational field given by a Bianchi type-I cosmological model filled with perfect fluid. The interacting term in the Lagrangian is chosen in the form of derivative coupling, i.e., L int = λ 2 ϕ ,α ϕ ,α F, with F being a function of the invariants I an J constructed from bilinear spinor forms S and P. We consider the cases when F is the power or trigonometric functions of its arguments. Self-consistent solutions to the spinor, scalar and BI gravitational field equations are obtained. The problems of initial singularity and asymptotically isotropization process of the initially anisotropic space-time are studied. It is also shown that the introduction of the Cosmological constant (Λ-term) in the Lagrangian generates oscillations of the BI model, which is not the case in absence of Λ term. Unlike the case when spinor field nonlinearity is induced by self-action, in the case in question, wehere nonlinearity is induced by the scalar field, there exist regular solutions even without broken dominant energy condition.

We study equilibrium configurations of boson stars in the framework of a class scalar-tensor theories of gravity with massive gravitational scalar (dilaton). In particular we investigate the influence of the mass of the dilaton on the boson star structure. We find that the masses of the boson stars in presence of dilaton are close to those in general relativity and they are sensitive to the ratio of the boson mass to the dilaton mass within a typical few percent. It turns out also that the boson star structure is mainly sensitive to the mass term of the dilaton potential rather to the exact form of the potential.Comment: 9 pages, latex, 9 figures, one figure dropped, new comments added, new references added, typos correcte

We develop the general theory of stars in Saa's model of gravity with propagating torsion and study the basic stationary state of a neutron star. Our numerical results show that the torsion force decreases the role of the gravity in the star configuration, leading to significant changes in the neutron star masses depending on the equation of state of star matter. The inconsistency of Saa's model with Roll - Krotkov - Dicke and Braginsky - Panov experiments is discussed.

We numerically construct static and spherically symmetric electrically charged black hole solutions in Einstein–Born–Infeld gravity with massive dilaton. The numerical solutions show that the dilaton potential allows many more black hole causal structures than the massless dilaton. We find that depending on the black hole mass and charge and the dilaton mass, the black holes can have either one, two, or three horizons. The extremal solutions are also found. As an interesting peculiarity we note that there are extremal black holes with an inner horizon and with triply degenerated horizon.

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