Matter collineation
A matter collineation (sometimes matter symmetry and abbreviated to MC) is a vector field that satisfies the condition, L X T a b = 0 {\displaystyle {\mathcal {L}}_{X}T_{ab}=0} where T a b {\displaystyle T_{ab}} are the energy–momentum tensor components. There is a "general plain symmetric metric" and 10 "equations for plane symmetric spacetime".