Semi-Analytic Stellar Structure in Scalar-Tensor Gravity

TL;DR

This paper develops semi-analytic methods to analyze how scalar-tensor gravity theories affect stellar structure, providing insights into the dependence of observable stellar parameters on microscopic scalar couplings.

Contribution

It introduces quasi-analytic techniques for solving stellar structure equations in scalar-tensor gravity, extending previous models and applying them to both toy and realistic neutron star scenarios.

Findings

Derived relations between stellar parameters and scalar couplings.

Explicit solutions for constant-density star models.

Comparison of toy models with realistic neutron star equations of state.

Abstract

Precision tests of gravity can be used to constrain the properties of hypothetical very light scalar fields, but these tests depend crucially on how macroscopic astrophysical objects couple to the new scalar field. We develop quasi-analytic methods for solving the equations of stellar structure using scalar-tensor gravity, with the goal of seeing how stellar properties depend on assumptions made about the scalar coupling at a microscopic level. We illustrate these methods by applying them to Brans-Dicke scalars, and their generalization in which the scalar-matter coupling is a weak function of the scalar field. The four observable parameters that characterize the fields external to a spherically symmetric star (the stellar radius, R, mass, M, scalar `charge', Q, and the scalar's asymptotic value, phi_infty) are subject to two relations because of the matching to the interior solution, generalizing the usual mass-radius, M(R), relation of General Relativity. We identify how these relations depend on the microscopic scalar couplings, agreeing with earlier workers when comparisons are possible. Explicit analytical solutions are obtained for the instructive toy model of constant-density stars, whose properties we compare to more realistic equations of state for neutron star models.