New Numerical Algorithm for Modeling of Boson-Fermion Stars in Dilatonic Gravity

TL;DR

The paper addresses modeling static, mixed boson-fermion stars in scalar-tensor gravity with a massive dilaton by formulating a two-domain free-boundary eigenproblem with unknown radius $R_s$ and spectral parameter $\Omega$. It develops a continuous analogue of Newton method (CANM) combined with a Landau transformation to fix the domain, solving coupled interior/exterior BVPs and a nonlinear algebraic system for $(R_s,\Omega,\varphi_s)$. Through a concrete scalar-tensor model, it demonstrates how to obtain profiles for the boson field $\sigma(x)$, the dilaton $\varphi(x)$, and the metric functions, and computes the dimensionless masses $M$, $M_{RB}$, and $M_{RF}$, identifying a cusp in the binding-energy diagram that marks a stability boundary. The methodology provides a robust framework for exploring strong-field effects in dilatonic gravity and mixed boson-fermion stars beyond General Relativity.

Abstract

We investigate numerically a models of the static spherically symmetric boson-fermion stars in 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 with unknown internal boundary. We employ the Continuous Analogue of Newton Method (CANM) which leads on each iteration to two separate linear boundary value problems with different dimensions inside and outside the star, respectively. Along with them a nonlinear algebraic system for the spectral parameters - radius of the star $R_{s}$ and quantity $Ω$ is solved also. In this way we obtain the behaviour of the basic geometric quantities and functions describing dilaton field and matter fields which build the star.

Figures (6)

• Figure 1: The function $\sigma(x)$ for $\sigma_c = 0.4$; $\mu_c =1.2$.
• Figure 2: The function $\varphi(x)$ for $\sigma_c = 0.4$; $\mu_c = 1.2$.
• Figure 3: The function $\nu(x)$ for $\sigma_c = 0.4$; $\mu_c = 1.2$.
• Figure 4: The function $\mu(x)$ for $\sigma_c = 0.4$; $\mu_c = 1.2$.
• Figure 5: The star mass $M$ and the rest fermion mass $M_{RF}$ as functions of the central value $\mu_c$