Energymomentum tensor and duality symmetry of linearized gravity in a Maxwellian formalism
Abstract
A Maxwelllike formulation of linearized gravity in flat background, based on the Fierz tensor as the analogue of the electromagnetic field strength, is discussed in detail and used to study fundamental properties of the linearized gravitational field. In particular, the linearized Einstein equations are formulated as first order partial differential equations in terms of the Fierz tensor, in analogy with the first order Maxwell equations. An energymomentum tensor ($T_{\mathrm{lg}}^{ab}$) is found for the linearized gravitational field, with properties that allow it to be regarded as a unique analogue of the standard energymomentum tensor of the electromagnetic field. $T_{\mathrm{lg}}^{ab}$ is quadratic in the Fierz tensor (which is constructed from the first derivatives of the linearized metric), traceless, and satisfies the dominant energy condition in a gauge that contains the transverse traceless gauge. In generalized harmonic gauges two additional symmetric energymomentum tensors are found that are analogous to some extent to the energymomentum tensor of the electromagnetic field. It is further shown that in suitable gauges, including the transverse traceless gauge, linearized gravity in the absence of matter has a duality symmetry that maps the Fierz tensor, which is antisymmetric in its first two indices, into its dual. Conserved currents associated with the gauge and duality symmetries of linearized gravity are also determined. These currents show good analogy with the corresponding currents in electrodynamics.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.02124
 Bibcode:
 2021arXiv210802124T
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 45 pages, minor corrections in the text, 2 references added, results unchanged