In [1,Chap.19.2] (see also [1, App.K.6]) M.W. Evans defines the term "free space" by the validity of

        d Ù F^a = A^(o) (R^a_b Ù A^b − ω^a_b Ù F^b) = µ_o j^a = 0                     (19.4)

where F^a denotes the 2-form of the electromagnetic field. Since Evans generally assumes F^a = A^(o) τ^a and A^a = A^(o) q^a we obtain the free space condition

        d Ù τ^a = 0                                                                                 (19.4')

or by referring to the 1st Bianchi identity [3] d Ù τ^a + ω^a_b Ù τ^b = R^a_b Ù q^b

... Eq.(19.4) is the experimental constraint:

        R^a_b Ù q^b = ω^a_b Ù τ^b                                                                 (19.6)

or free space condition.

However, none of the eqs.(19.4) and (19.6) transforms Lorentz covariantly as can be seen from the "free space condition" written as dÙτ=0.

Evans' concept of "free space" is not Lorentz invariant.

Evans continues:

Using the Maurer-Cartan structure equations:

        τ^b = D Ù q^b                                                                              (19.7)

        R^a_b = D Ù ω^a_b                                                                         (19.8)

it is seen that a particular solution of Eq. (19.6) is:

        ω^a_b = − ½ κ Î^a_bc q^c                                                               (19.9)

However, Eq.(19.6) is an equation of 4D where no 3-index Î-tensor can be defined [2].

Thus, Evans' particular solution (19.9) doesn't exist.