  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.
