Different representations of the Levi-Civita Bertotti Robinson solution
Journal article, Peer reviewed
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https://hdl.handle.net/10642/1532Utgivelsesdato
2013-04-23Metadata
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Originalversjon
Grøn, Ø. & Johannesen, S. (2013).Different representations of the Levi-Civita Bertotti Robinson solution. The European Physical Journal Plus, 128 (-43) http://dx.doi.org/10.1140/epjp/i2013-13043-ySammendrag
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.