Imbedding a Reissner-Nordstr\"om charged mass into cosmology

TL;DR

This paper extends a method for embedding a mass into cosmology to include a Reissner-Nordström charged mass, analyzing its effects on orbital dynamics and providing new metrics for zero-curvature cosmological scenarios.

Contribution

It introduces a novel approach to embed a charged mass into cosmological models and derives metrics and orbital equations considering electric charge effects.

Findings

Orbits spiral when a charged mass is embedded in cosmology.

Derived generalized orbital radius change equation.

Discussed limitations of Newtonian approximations.

Abstract

We present the extension of the method of imbedding a mass into cosmology proposed by Gautreau, for the case of a Reissner-Nordstr\"om charged mass. We work in curvature coordinates $(R,T)$ where the coordinate time $T$ is measured by clocks at fixed points $R = $ const., and geodesic coordinates $(R,\tau)$ where $\tau$ is the time recorded by clocks moving along the radial geodesics. The Einstein equations are solved for a energy-momentum tensor which is composed of a cosmological fluid and an electrostatic field outside a radius $R_{b}$. Inside $R_{b}$ we have a part of cosmological fluid plus a Reissner-Nordstr\"om charged mass. We offer metrics for a Reissner-Nordstr\"om charged mass imbedded into different cosmological scenarios with zero curvature. An important consequence of our results, is that orbits will spiral when a charged mass is imbedded into a cosmological background. We found the generalized equation for the change of orbital radius, by using geodesic coordinates. Some criticism to the Newtonian calculation done by Gautreau for the orbital spiralling is discussed.