The above is the general transformation of a skew symmetric contravariant tensor for a rapidity of θ along the x axis where C = cosh(θ) and S = sinh(θ).

Applying this to the electromagnetic tensor gives us:
E'_x = E_x
E'_y = CE_y + SB_z
E'_z = CE_z − SB_y
B'_x = B_x
B'_y = CB_y − SE_z
B'_z = CB_z + SE_y

This must be used in the context of
t' = Ct + Sx
x' = Cx + St
y' = y
z' = z

It would be good to see that a solution of Maxwell’s equations hereby transforms into another solution!