A Free Boundary Problem in the Theory of the Stars

TL;DR

The paper addresses modeling static, mixed boson-fermion stars in scalar-tensor gravity with a massive dilaton by formulating it as a nonlinear free-boundary, two-parameter eigenproblem with unknown radius R_s and frequency Omega. It introduces a solution framework based on the Continuous Analogue of Newton Method to couple interior and exterior solutions across the unknown boundary, using a Landau transformation to map the problem to an interior domain. Numerical results for a concrete model reveal a cusp in the binding-energy diagram, indicating a stability transition and possible gravitational collapse beyond the cusp. The work provides a robust computational approach for free-boundary spectral problems in relativistic stars and offers insights into dark-matter–like configurations within scalar-tensor theories.

Abstract

We investigate numerically 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 with unknown internal boundary. To solve this problem the Continuous Analogue of Newton Method is used.

Figures (2)

• Figure 1: The star mass $M$ and the rest fermion mass $M_{RF}$ as functions of the central value $\mu_c$.
• Figure 2: The binding energy $E$ versus the rest fermion mass $M_{RF}$.