Spherically symmetric massive scalar fields in GR

TL;DR

This paper reviews spherically symmetric solutions in Einstein's gravity with scalar fields, discusses the limitations of existing solutions, and introduces a series solution for homogeneous isotropic scalar fields, analyzing stability and gravitational effects.

Contribution

It presents a new series solution for static, homogeneous isotropic scalar fields with mass and cosmological constant, expanding understanding of scalar field effects in GR.

Findings

Mass of scalar field eliminates local gravitational effects.

Series solution exists for homogeneous isotropic scalar fields.

System is shown to be unstable via dynamical systems analysis.

Abstract

First we review some of the attempts made to find exact spherically symmetric solutions of Einstein field equations in the presence of scalar fields .Wyman solution in both static and non static scalar field is discussed briefly and it is show that why in the case of non static homogenous matter field, static metric can not be represented in terms of elementary functions. We mention here that if our spacetime be static, according to EFE there is two option for choose scalar field matter: static (time independent) and non static (time dependent). All these solutions are limited to the minimally coupled massless scalar fields and also in the absence of the cosmological constant . Then we show that if we are interesting to have a homogenous isotropic scalar field matter one can construct a series solution in terms of scalar field's mass and cosmological constant. This metric is static and posses a locally flat case as a special chooses of mass of scalar field and can be interpreted as an effective vacuum. Therefore mass of scalar field eliminates any locally gravitational effect as tidal forces. Finally we describe why this system is unstable in the language of dynamical systems.