  A formulation of linearized gravity in flat background, based on the Fierz
tensor as a counterpart 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 written as first
order partial differential equations in terms of the Fierz tensor, in analogy
with the first order Maxwell equations. An energy-momentum tensor
($T_{\mathrm{lg}}^{ab}$) with favourable properties and exhibiting remarkable
similarity to the standard energy-momentum tensor of the electromagnetic field
is found for the linearized gravitational 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. 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.
