Curiel, Erik (2014) On Geometric Objects, the NonExistence of a Gravitational StressEnergy Tensor, and the Uniqueness of the Einstein Field Equation. [Preprint]

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Abstract
The question of the existence of gravitational stressenergy in
general relativity has exercised investigators in the field since
the inception of the theory. Folklore has it that no adequate
definition of a localized gravitational stressenergetic quantity
can be given. Most arguments to that effect invoke one version or
another of the Principle of Equivalence. I argue that not only are
such arguments of necessity vague and handwaving but, worse, are
beside the point and do not address the heart of the issue. Based
on a novel analysis of what it may mean for one tensor to depend in
the proper way on another, which, en passant, provides a
precise characterization of the idea of a "geometric object", I
prove that, under certain natural conditions, there can be no tensor
whose interpretation could be that it represents gravitational
stressenergy in general relativity. It follows that gravitational
energy, such as it is in general relativity, is necessarily
nonlocal. Along the way, I prove a result of some interest in own
right about the structure of the associated jet bundles of the
bundle of Lorentz metrics over spacetime. I conclude by showing
that my results also imply that, under a few natural conditions, the
Einstein field equation is the unique equation relating
gravitational phenomena to spatiotemporal structure, and discuss how
this relates to the nonlocalizability of gravitational
stressenergy.
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Item Type:  Preprint  

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Keywords:  gravitational energy; stressenergy tensors; concomitants; jet bundles; principle of equivalence; geometric objects; Einstein field equation  
Subjects:  Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Relativity Theory 

Depositing User:  Dr. Erik Curiel  
Date Deposited:  30 Aug 2014 00:20  
Last Modified:  30 Aug 2014 00:20  
Item ID:  10985  
Official URL:  http://strangebeautiful.com/papers/curielnonexist...  
Subjects:  Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Relativity Theory 

Date:  August 2014  
URI:  http://philsciarchive.pitt.edu/id/eprint/10985 
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