PhilSci Archive

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]

[img] PDF
simple-proof-uniq-efe-all-dims.pdf - Submitted Version

Download (330kB)

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.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

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: https://philsci-archive.pitt.edu/id/eprint/11860

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item