Curiel, Erik (2016) A Simple Proof of the Uniqueness of the Einstein Field Equation in All Dimensions. [Preprint]
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Abstract
The standard argument for the uniqueness of the Einstein field
equation is based on Lovelock's Theorem, the relevant statement of
which is restricted to four dimensions. I prove a theorem similar
to Lovelock's, with a physically modified assumption: that the
geometric object representing curvature in the Einstein field
equation ought to have the physical dimension of stressenergy. The
theorem is stronger than Lovelock's in two ways: it holds in all
dimensions, and so supports a generalized argument for uniqueness;
it does not assume that the desired tensor depends on the metric
only up secondorder partialderivatives, that condition being a
consequence of the proof. This has consequences for understanding
the nature of the cosmological constant and theories of
higherdimensional gravity. Another consequence of the theorem is
that it makes precise the sense in which there can be no
gravitational stressenergy tensor in general relativity. Along the
way, I prove a result of some interest about the second jetbundle
of the bundle of metrics over a manifold.
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Item Type:  Preprint  

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Keywords:  Einstein field equation; stressenergy tensors; concomitants; jet bundles; gravitational energy; Lovelock's Theorem  
Subjects:  General Issues > Laws of Nature Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory General Issues > Structure of Theories 

Depositing User:  Dr. Erik Curiel  
Date Deposited:  13 Jan 2016 16:08  
Last Modified:  13 Jan 2016 16:08  
Item ID:  11860  
Subjects:  General Issues > Laws of Nature Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory General Issues > Structure of Theories 

Date:  January 2016  
URI:  http://philsciarchive.pitt.edu/id/eprint/11860 
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