2002/02/20 by José M. M. Senovilla, J. M. M. Senovilla, Senovilla, J. M. M.
Mathematics · Physics and Astronomy · #53B30 #83C99 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #gr-qc #math-ph #math.DG #math.MP #msc:53B30 #msc:83C99
paper · pdf · doi:10.48550/arxiv.math-ph/0202029
20 pages, no figures; Invited lecture presented at the 1st Conference on Lorentzian Geometry, "Benalmadena 2001"
arxiv created 2002/02/20 · openalex publication_date 2002/02/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.