Curiel, Erik (2018) 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. The main theorem proven underlying all the arguments
is considerably stronger than the standard result in the literature
used for the same purposes (Lovelock's theorem of 1972): it holds in
all dimensions (not only in four); it does not require an assumption
about the differential order of the desired concomitant of the
metric; and it has a more natural physical interpretation.
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Item Type:  Preprint  

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Additional Information:  Forthcoming in *Studies in History and Philosophy of Modern Physics*, 2018  
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:  29 Aug 2018 00:03  
Last Modified:  29 Aug 2018 00:03  
Item ID:  14980  
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 2018  
URI:  http://philsciarchive.pitt.edu/id/eprint/14980 
Available Versions of this Item

On Geometric Objects, the NonExistence of a Gravitational StressEnergy Tensor, and the Uniqueness of the Einstein
Field Equation. (deposited 30 Aug 2014 00:20)
 On Geometric Objects, the NonExistence of a Gravitational StressEnergy Tensor, and the Uniqueness of the Einstein Field Equation. (deposited 29 Aug 2018 00:03) [Currently Displayed]
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