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Title: Covariant energy–momentum and an uncertainty principle for general relativity

We introduce a naturally-defined totally invariant spacetime energy expression for general relativity incorporating the contribution from gravity. The extension links seamlessly to the action integral for the gravitational field. The demand that the general expression for arbitrary systems reduces to the Tolman integral in the case of stationary bounded distributions, leads to the matter-localized Ricci integral for energy–momentum in support of the energy localization hypothesis. The role of the observer is addressed and as an extension of the special relativistic case, the field of observers comoving with the matter is seen to compute the intrinsic global energy of a system. The new localized energy supports the Bonnor claim that the Szekeres collapsing dust solutions are energy-conserving. It is suggested that in the extreme of strong gravity, the Heisenberg Uncertainty Principle be generalized in terms of spacetime energy–momentum. -- Highlights: •We present a totally invariant spacetime energy expression for general relativity incorporating the contribution from gravity. •Demand for the general expression to reduce to the Tolman integral for stationary systems supports the Ricci integral as energy–momentum. •Localized energy via the Ricci integral is consistent with the energy localization hypothesis. •New localized energy supports the Bonnor claim that the Szekeres collapsing dustmore » solutions are energy-conserving. •Suggest the Heisenberg Uncertainty Principle be generalized in terms of spacetime energy–momentum in strong gravity extreme.« less
Authors:
 [1] ;  [2]
  1. Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, B.C. V8W 3P6 (Canada)
  2. Department of Mathematics, Tulane University, New Orleans, LA 70118 (United States)
Publication Date:
OSTI Identifier:
22224270
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 339; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACTION INTEGRAL; DEMAND; GENERAL RELATIVITY THEORY; GRAVITATIONAL FIELDS; HYPOTHESIS; MATHEMATICAL SOLUTIONS; MATTER; RELATIVISTIC RANGE; SPACE-TIME; UNCERTAINTY PRINCIPLE