Real scalar field stars of the EKG equations including matter

TL;DR

This paper explores static solutions of the Einstein-Klein-Gordon equations with matter, revealing that photon-like gases can produce nearly constant gravitational fields at large distances, potentially explaining dark matter effects.

Contribution

It introduces a coupling in the EKG equations for real scalar fields with matter, enabling static solutions and revealing new gravitational phenomena related to photon-like gases.

Findings

Photon-like gases produce nearly constant gravitational fields at large distances.

The gravitational field may generate a bounding attraction that prevents unlimited mass increase.

A method is proposed to evaluate the effects of photon bounding on gravitational fields.

Abstract

Static (not stationary) solutions of the Einstein-Klein-Gordon (EKG) equations including matter are obtained for real scalar fields. The scalar field interaction with matter is considered. The introduced coupling allows the existence of static solutions in contraposition with the case of the simpler EKG equations for real scalar fields and gravity. Surprisingly, when the considered matter is a photon-like gas, it turns out that the gravitational field intensity at large radial distances becomes nearly a constant, exerting an approximately fixed force to small bodies at any distance. The effect is clearly related with the massless character of the photon-like field. It is also argued that the gravitational field can generate a bounding attraction, that could avoid the unlimited increase in mass with the radius of the obtained here solution. This phenomenon, if verified, may furnish a possible mechanism for explaining how the increasing gravitational potential associated to dark matter, finally decays at large distances from the galaxies. A method for evaluating these photon bounding effects is just formulated in order to be further investigated.