In these definitions, R a b could be replaced by its trace-free part Q a b = R a b − − 1 4 g a b R or by the Einstein tensor G a b = R a b − − 1 2 g a b R because of the normalization relations. Also, Φ Φ 11 is reduced to Φ Φ 11 = 1 2 R a b l a n b = 1 2 R a b m a m ¯ ¯ b for electrovacuum ( Λ Λ = 0 ).