In keeping with the formalism's practice of using distinct unindexed symbols for each component of an object, the covariant derivative operator ∇ ∇ a is expressed using four separate symbols ( D , Δ Δ , δ δ , δ δ ¯ ¯ ) which name a directional covariant derivative operator for each tetrad direction. Given a linear combination of tetrad vectors, X a = a l a + b n a + c m a + d m ¯ ¯ a , the covariant derivative operator in the X a direction is ∇ ∇ X = X a ∇ ∇ a = ( a D + b Δ Δ + c δ δ + d δ δ ¯ ¯ ) .