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GR: Gravitation und Relativitätstheorie

GR 7: Grundlegende Probleme und allgemeiner Formalismus

GR 7.2: Fachvortrag

Donnerstag, 18. März 2004, 09:20–09:40, H20

Bel-Robinson, Bach, Cotton and superenergy tensors — •Christian Heinicke — Institut für Theoretische Physik, Universität zu Köln, 50923 Köln

We investigate the relation between the Bel-Robinson, the Bach and the Cotton tensors.

For n=3, the Cotton tensor is conserved. In n=4, the Bach tensor is conserved, as well as the Bel-Robinson tensor in case of vacuum spacetimes. By means of the Einstein equation these “geometrical” conservation laws lead to corresponding conservation laws for “matter superenergy tensors”.

In particular, we will discuss the Chevreton superenergy tensor of the source-free electromagnetic field which recently attracted attention in the literature.

[1]A. A. García, F. W. Hehl, C. Heinicke, A. Macías: The Cotton tensor in Riemannian spacetime. Class. Quant. Grav.  (2004), gr-qc/0309008

[2] S. B. Edgar: On the structure of the new electromagentic conservation laws. gr-qc/0311035