Other
Scientific paper
May 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998gregr..30..695d&link_type=abstract
General Relativity and Gravitation, Volume 30, Issue 5, pp.695-700
Other
3
Scientific paper
Brinkmann has shown that conformally related Einstein spaces are either Ricci flat pp-waves or conformally flat spaces with one as de Sitter space and the other being flat. We herewith show that if gikand overline g _{ik} left( { = left( {1/w^2 } right)g_{ik} } right)are distinct metrics for which G_{ik} = overline G _{ik}, then both represent (generalised) pp-waves; and w,iis a homothetic conformal Killing vector of gik. It is further observed that in the situation G_{ik} = overline G _{ik} + Λ overline g _{ik}we can have many (and also non-conformally flat) conformally related solutions, unlike in Einstein spaces. In particular for perfect fluid coupling, we show that the conformally related solutions have to be Friedman-Robertson-Walker metrics with equation of state as μ + 3p = 0,μ = p, or pp-waves depending on whether w,iis timelike, spacelike or null.
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