  The Levi-Civita Bertotti Robinson (LBR) spacetime is investigated in various
coordinate systems. By means of a general formalism for constructing
coordinates in conformally flat spacetimes, coordinate transformations between
the different coordinate systems are deduced. We discuss the motion of the
reference frames in which the different coordinate systems are comoving.
Furthermore we characterize the motion of the different reference frames by
their normalized timelike Killing vector fields, i.e. by the four velocity
fields of the reference particles. We also deduce the formulae in the different
coordinate systems for the embedding of the LBR spacetime in a flat
6-dimensional manifold. In particular we discuss a scenario with a spherical
domain wall having LBR spacetime outside the wall and flat spacetime inside. We
also discuss the internal flat spacetime using the same coordinate systems as
in the external LBR spacetime with continuous metric at the wall. Among the
different cases one represents a Milne-LBR universe model with a part of the
Milne universe inside the wall and an infinitely extended LBR universe outside
it. In an appendix we define combinations of trigonometric and hyperbolic
functions that we call k-functions and present a new k-function calculus.
