On Hypermomentum in General Relativity I. The Notion of Hypermomentum

Abstract In this series of notes, we introduce a new quantity into the theory of classical matter fields. Besides the usual energy-momentum tensor, we postulate the existence of a further dynamical attribute of matter, the 3rd rank tensor ⊿ ijk of hypermomentum. Subsequently, a general relativistic field theory of energy-momentum and hypermomentum is outlined. In Part I we motivate the need for hypermomentum. We split it into spin angular momentum, the dilatation hypermomentum, and traceless proper hypermomentum and discuss their physical meanings and conservation laws.

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