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

Understand

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.