Numerical Approach to the Exterior Solution of Spherically Symmetric and Static Configuration in Scalar-Tensor Theories

TL;DR

This paper develops a numerical method to approximate the exterior solutions of spherically symmetric, static scalar-tensor configurations, providing parameter-independent analytical expressions with high accuracy.

Contribution

It introduces a way to fit numerical solutions with approximate analytical formulas that are weakly dependent on model parameters in scalar-tensor theories.

Findings

Exterior solutions can be expressed with parameter-independent formulas

Achieved approximation accuracy around 10^{-5}

Provided explicit functions for scalar field and metric in terms of mass and radius

Abstract

We numerically examine the exterior solution of spherically symmetric and static configuration in scalar-tensor theories by using the nonminimally coupled scalar field with zero potential as our sample model. Our main purpose in this work is to fit the resulting data of the numerical solutions in the interested region by seeking for approximate analytical expressions which are weakly dependent of the parameters of a model, such as the nonminimal coupling constant in the present case. To this end, we determine the main forms of the mass and the metric functions in terms of the scalar field and their surface values. Then, we provide a function for the scalar field that contains only the mass and the radius of the configuration together with the surface and the asymptotic values of the scalar field. Therefore, we show that the exterior solution can be expressed in a form which does not depend on the parameters of a chosen model up to an order of accuracy around $10^{-5}$.