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A rank-n tensor on a Lorentzian manifold V whose contraction with n arbitrarycausal future directed vectors is non-negative is said to have the dominantproperty. These tensors, up to sign, are called causal tensors, and wedetermine their general properties in dimension N. We prove that rank-2 tensorswhich map the null cone on itself are causal. It is known that, to any tensor Aon V there is a corresponding ``superenergy'' (s-e) tensor T{A} which alwayshas the dominant property. We prove that, conversely, any symmetric rank-2tensor with the dominant property can be written in a canonical way as a sum ofN s-e tensors of simple forms. We show that the square of any rank-2 s-e tensoris proportional to the metric if N<5, and that this holds for the s-e tensor ofany simple form for arbitrary N. Conversely, we prove that any symmetric rank-2tensor T whose square is proportional to the metric must be, up to sign, thes-e of a simple p-form, and that the trace of T determines the rank p of theform. This generalises, both with respect to N and the rank p, the classicalalgebraic Rainich conditions, which are necessary and sufficient conditions fora metric to originate in some physical field, and has a geometricinterpretation: the set of s-e tensors of simple forms is precisely the set oftensors which preserve the null cone and its time orientation. It also meansthat all involutory Lorentz transformations (LT) can be represented as s-etensors of simple forms, and that any rank-2 s-e tensor is the sum of at most Nconformally involutory LT. Non-symmetric null cone preserving maps are shown tohave a causal symmetric part and are classified according to the nulleigenvectors of the skew-symmetric part. We thus obtain a completeclassification of all conformal LT and singular null cone preserving maps on V.Comment: 36 pages, no figures, LaTeX fil

Null cone preserving maps, causal tensors and algebraic Rainich theory