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Observations on the Equivalence of the Harmonic Gauge Constraint and Global Energy-Momentum Conservation in General Relativity

Author:

McAlea, Eamon

Category:

Research Papers

Sub-Category:

Relativity Theory

Language:

English

Date Published:

December 2, 2011

File:

/Research Papers-Relativity Theory/Download/3809

Downloads:

988

Keywords:

Kerr Metric, Harmonic Gauge, Global Conservation, General Relativity, Wave Equation, Lorentz Transformation, Lorentz Invariance, Galilean Transformation

Abstract:

It is here demonstrated that by constraining the Einstein Field Equations (EFE) with the Harmonic Gauge condition results in not only the well established implication that the EFE are nothing more than wave equations, but also in the fact of the existence of a global conservation of energy and momentum law comprised of both matter and fields, with the fields being defined in terms of the underlying metric. This result is well known to practitioners of General Relativity, and it is the purpose of this paper to show rather explicitly how it is done, especially for the benefit of beginners to the field in as simple a manner as the machinery of Tensor Calculus will permit. It is also speculated, but not elaborated upon here, that the various pseudo tensor approaches to construct global conservation equations are equivalent to the EFE with a corresponding attached gauge constraint, but which may not necessarily in each case correspond to a wave like equation, unlike the case for the Harmonic Gauge

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