Additionally, the covariant Maxwell equations are also applicable in free space: F α α β β ; β β = 0 F [ α α β β ; γ γ ] = 1 3 ( F α α β β ; γ γ + F β β γ γ ; α α + F γ γ α α ; β β ) = 1 3 ( F α α β β , γ γ + F β β γ γ , α α + F γ γ α α , β β ) = 0. where the semicolon represents a covariant derivative, and the brackets denote anti-symmetrization. The first equation asserts that the 4- divergence of the 2-form F is zero, and the second that its exterior derivative is zero. From the latter, it follows by the Poincaré lemma that in a coordinate chart it is possible to introduce an electromagnetic field potential A α such that F α α β β = A α α ; β β − − A β β ; α α = A α α , β β − − A β β , α α in which the comma denotes a partial derivative. This is often taken as equivalent to the covariant Maxwell equation from which it is derived. However, there are global solutions of the equation that may lack a globally defined potential.