Mathematical Modeling of Boson–Fermion Stars in the Generalized Scalar–Tensor Theories of Gravity

A model of static boson–fermion stars with spherical symmetry based on the scalar–tensor theory of gravity with a massive dilaton field is investigated numerically. Since the radius of the star is a priori an unknown quantity, the corresponding boundary value problem is treated as a nonlinear spectral problem with a free internal boundary. The continuous analogue of Newton method is used to solve this problem. Information about basic geometric functions and the functions describing the matter fields which build the star is obtained. From a physical point of view the main result is that the structure and properties of the star in the presence of a massive dilaton field depend essentially on both its fermionic and bosonic comp-onents.