On the conservation of superenergy and its applications
Abstract
In this work we present a geometric identity involving the BelRobinson tensor which is formally similar to the Sparling identity (which involves the Einstein tensor through the Einstein 3form). In our identity the BelRobinson tensor enters through the BelRobinson 3form which, we believe, is introduced in the literature for the first time. The meaning of this identity is that it is possible to formulate a generic conservation law for the quantity represented by the BelRobinson tensor (superenergy). We also show how one can use the BelRobinson 3form to estimate the components of the BelRobinson tensor which are computed with respect to the causal elements of a frame. This estimate could be useful in a global existence proof of the solutions of a theory of gravitation in dimension four.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 July 2014
 DOI:
 10.1088/02649381/31/13/135008
 arXiv:
 arXiv:1308.4390
 Bibcode:
 2014CQGra..31m5008G
 Keywords:

 conserved current;
 superenergy estimate;
 BelRobinson tensor;
 83C40;
 83C05;
 General Relativity and Quantum Cosmology;
 83C40;
 83C05
 EPrint:
 11 pages, 1 figure. Section 5 is new. Minor change in the title to take this into account (see abstract). To appear in "Classical and Quantum Gravity"