New electromagnetic conservation laws

The Chevreton superenergy tensor was introduced in 1964 as a counterpart, for electromagnetic fields, of the well-known Bel-Robinson tensor of the gravitational field. We here prove the unnoticed facts that, in the absence of electromagnetic currents, Chevreton’s tensor (i) is completely symmetric, and (ii) has a trace-free divergence if Einstein-Maxwell equations hold. It follows that the trace of the Chevreton tensor is a rank-2, symmetric, trace-free, conserved tensor, which is different from the energy-momentum tensor, and nonetheless can be constructed for any test Maxwell field, or any Einstein-Maxwell spacetime. 1 The Bel-Robinson “superenergy ” tensor [2, 4] is today a well-known tool in General Relativity. Despite the lack of a conclusive physical meaning, it has been proved as very valuable in many mathematical developments and theoretical applications, see e.g.[13, 15] and references therein. The analogy of many of its properties with those of the energy-momentum tensor of electromagnetic fields is intriguing and certainly suggestive, something which has led many authors to look for similar superenergy tensors of fields other than the graviational one (e.g [7, 13, 15, 16] and references therein). Perhaps the first such attempt appears in the work