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

Abstract

A model of static boson-fermion star with spherical symmetry based on the scalar-tensor theory of gravity with massive dilaton field is investigated numerically.Since the radius of star is a priori an unknown quantity, the corresponding boundary value problem (BVP) is treated as a nonlinear spectral problem with a free internal boundary. The Continuous Analogue of Newton Method (CANM) for solving this problem is applied.Information about basic geometric functions and the functions describing the matter fields, which build the star is obtained. In a physical point of view the main result is that the structure and properties of the star in presence of massive dilaton field depend essentially both of its fermionic and bosonic components.Keywords. boson-fermion star, scalar-tensor theory of gravity, massive dilaton field, twoparametric nonlinear spectral problem, continuous analog of Newton method, method of splinecollocation.

A numerical algorithm for modelling of boson–fermion stars in dilatonic gravity

“…x . For example when x ≈ 9 the derivative ν ′ (x) ≈ 10 −2 , while for x > 27 ν ′ (x) < 10 −4 , i.e., the asymptotical behaviour of calculated grid function and its derivative agrees very well with the theoretical prediction (see [3]). The function ϕ(x) increases rapidly for x < 4, besides that it trends asymptotically to zero.…”

“…The function ϕ(x) increases rapidly for x < 4, besides that it trends asymptotically to zero. Obviously the quantitative behaviour of ϕ(x) for central value σ c = 0.4 is determinated by the dominance of the term B T over the term F T (see [3]). At last the function µ(x) is nontrivial in the inner domain x ∈ [0, 1], i.e.…”

“…Here we aim at applying the new solving method to the above formulated problem. This method differs from that one proposed in [3] and for the governing field equations written in the forms (7) and (10) it possesses certain advantage.…”

“…In this paper we present a numerical method for solving the equations of the general scalar-tensor theories of gravity including a dilaton potential term for the general case of mixed boson-fermion star. This method is an impruvment of the method concerning the similar problem proposed in our recent work [3]. The original domain is splitted to two domains: inner inside the star and external outside the star.…”

On the effect of anisotropy on stellar models

“…The most of the proposed models to describe this kind of objects require an analysis starting of an adequate gravitational theory, at these order the description of compact objects in hydrostatic equilibrium must be treated in a relativistic way, however, there are analysis made under the assumption of different gravitational theories [10][11][12]. In the case of the Einstein's equations with a perfect fluid as the source of matter the Tolman Oppenheimer Volkof [13,14] allows to determinate the mass, radio and central density of the stars from the state equation using numerical methods [15].…”