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2016 ; 113
(42
): 11662-11666
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English Wikipedia
Simplified derivation of the gravitational wave stress tensor from the linearized
Einstein field equations
#MMPMID27698143
Balbus SA
Proc Natl Acad Sci U S A
2016[Oct]; 113
(42
): 11662-11666
PMID27698143
show ga
A conserved stress energy tensor for weak field gravitational waves propagating
in vacuum is derived directly from the linearized general relativistic wave
equation alone, for an arbitrary gauge. In any harmonic gauge, the form of the
tensor leads directly to the classical expression for the outgoing wave energy.
The method described here, however, is a much simpler, shorter, and more
physically motivated approach than is the customary procedure, which involves a
lengthy and cumbersome second-order (in wave-amplitude) calculation starting with
the Einstein tensor. Our method has the added advantage of exhibiting the direct
coupling between the outgoing wave energy flux and the work done by the
gravitational field on the sources. For nonharmonic gauges, the directly derived
wave stress tensor has an apparent index asymmetry. This coordinate artifact may
be straightforwardly removed, and the symmetrized (still gauge-invariant) tensor
then takes on its widely used form. Angular momentum conservation follows
immediately. For any harmonic gauge, however, the stress tensor found is
manifestly symmetric from the start, and its derivation depends, in its entirety,
on the structure of the linearized wave equation.