Affiliations: [a] Faculty of Mathematics and Computer Science, University of Sofia, Sofia, Bulgaria | [b] Faculty of Applied Mathematics and Computer Science, Technical University of Sofia, Sofia, Bulgaria | [c] Faculty of Physics, University of Sofia, Sofia, Bulgaria
Correspondence:
[5]
The address for manuscript correspondence: Prof. Plamen P. Fiziev, Faculty of Physics, University of Sofia, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria. Tel.: +3592 626271. Fax: +3592 9625276. E-mail: fiziev@phys.uni-sofia.bg.
Note: [1] This work was supported by the Bulgarian National Scientific Fund, Contr. NoNo F610/99, MM602/96 and by the Sofia University Research Fund, Contr. No. 245/99.
Note: [2] E-mail: todorlb@fmi.uni-sofia.bg.
Note: [3] E-mail: mtod@vmei.acad.bg.
Note: [4] E-mail: fiziev@phys.uni-sofia.bg.
Note: [6] E-mail: yazad@phys.uni-sofia.bg.
Abstract: We investigate numerically models of static spherically symmetric boson-fermion stars in the scalar-tensor theory of gravity with a massive dilation field. The proper mathematical model of such stars is interpreted as a nonlinear two-parametric eigenvalue problem with an unknown internal boundary. To solve this problem, the Continuous Analogue of Newton Method (CANM) is employed. On each iteration CANM leads to two separate linear boundary value problems with different dimensions inside and outside the star. Along with them a nonlinear algebraic system for the spectral parameters is also solved. In this way, we determine the behaviour of the basic geometric quantities and functions describing the dilation field and matter fields building the star. Prom the physical point of view, the main result is that the structure and properties of such stars depend essentially both on their fermionic and bosonic components.
Keywords: Two-parametric nonlinear eigenvalue problem, continuous analog of the Newton method, mixed fermion-boson stars, scalar-tensor theory of gravity, massive dilation field
