  We present a deformation theory approach to the classification of kinematical
Lie algebras in 3+1 dimensions and present calculations leading to the
classifications of all deformations of the static kinematical Lie algebra and
of its universal central extension, up to isomorphism. In addition we determine
which of these Lie algebras admit an invariant symmetric inner product. Among
the new results, we find some deformations of the centrally extended static
kinematical Lie algebra which are extensions (but not central) of deformations
of the static kinematical Lie algebra. This paper lays the groundwork for two
companion papers which present similar classifications in dimension D + 1 for
all D>3 and in dimension 2+1.
