On the exponential of the 2-forms in relativity

A study of intrinsic properties of proper Lorentz tensors (tensor fields defining proper Lorentz transformations at every point of space-time) is made, giving rise to their covariant decompositions. The exponential series for a generic 2-form is covariantly summed, and the resulting proper Lorentz tensor is expressed as a linear combination of the metric tensor, the 2-form, its dual and its energy tensor. Some covariant expressions for the 2-form corresponding to the logarithmic branches of a proper Lorentz tensor are given. Some properties of the Lorentz group are easily found, concerning the surjectivity, local injectivity and local inversibility of the exponential map.