Superenergy tensors and their applications

Details Superenergy tensors and their applications Superenergy tensors and their applications

2002-02-20

arxiv.org/abs/math-ph/0202029v1

Physics

Mathematical Physics

20 pages, no figures; Invited lecture presented at the 1st Conference on Lorentzian Geometry, "Benalmadena 2001"

Scientific paper

In Lorentzian manifolds of any dimension the concept of causal tensors is introduced. Causal tensors have positivity properties analogous to the so-called ``dominant energy condition''. Further, it is shown how to build, from ANY given tensor $A$, a new tensor quadratic in $A$ and ``positive'', in the sense that it is causal. These tensors are called superenergy tensors due to historical reasons because they generalize the classical energy-momentum and Bel-Robinson constructions. Superenergy tensors are basically unique and with multiple and diverse physical and mathematical applications, such as: a) definition of new divergence-free currents, b) conservation laws in propagation of discontinuities of fields, c) the causal propagation of fields, d) null-cone preserving maps, e) generalized Rainich-like conditions, f) causal relations and transformations, and g) generalized symmetries. Among many others.

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