The classification of plane symmetric spacetimes by isometries

Abstract

A complete classification of plane symmetric Lorentzian manifolds according to their additional isometries and metrics (or classes of metrics) is obtained by solving the Killing equations. We obtain all metrics (or classes of metrics), that admit the group of motions Gr (where r=3,4,5,6,7 and 10) containing SO(2)⨷R2, the minimal symmetry inherited by the plane symmetric manifolds.