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A Simple Proof of the Uniqueness of the Einstein Field Equation in All Dimensions

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 stress-energy. 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 second-order partial-derivatives, that condition being a
consequence of the proof. This has consequences for understanding
the nature of the cosmological constant and theories of
higher-dimensional gravity. Another consequence of the theorem is
that it makes precise the sense in which there can be no
gravitational stress-energy tensor in general relativity. Along the
way, I prove a result of some interest about the second jet-bundle
of the bundle of metrics over a manifold.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Curiel, Erikerik@strangebeautiful.com
Keywords: Einstein field equation; stress-energy 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://philsci-archive.pitt.edu/id/eprint/11860

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