A numerical algorithm for modelling boson-fermion stars in dilatonic gravity

We investigate numerically the class of models of the static spherically symmetric boson-fermion stars in the scalar-tensor theory of gravity with massive dilaton field. The proper mathematical model of such stars is interpreted as a nonlinear two-parametric eigenvalue problem. The first of the parameters is the unknown internal boundary (the radius of the fermionic part of the star) R sub s , and the second one represents the frequency OMEGA of the time oscillations of the boson field. To solve this problem, the whole space [0, infinity) is splitted into two domains: internal [0, R sub s] (inside the star) and external [R sub s , infinity) (outside the star). In each domain the physical model leads to two nonlinear boundary value problems in respect to metric functions, the functions describing the fermionic and bosonic matter, and the dilaton field. These boundary value problems have different dimensions inside and outside the star, respectively. The solutions in these regions are obtained separately and matched using the necessary algebraic continuity conditions including R sub s and OMEGA. The continuous analogue of the Newton method for solving both the nonlinear differential and algebraic problems is used. The corresponding linearized boundary value problems at each iteration are solved by means of spline-collocation scheme. In this way, we obtain the behaviour of the basic geometric quantities and functions describing a dilaton field and matter fields, which build the star