Known as a symmetry of vacuum Maxwell equations, the electric-magnetic
duality can be lifted actually to a symmetry of an action. The Lagrangian of
this action is written in terms of two vector potentials, one electric and one
magnetic, and while it is manifestly invariant under duality rotations, it is
not manifestly Lorentz covariant. This duality symmetry exists also in
linearized gravity in four dimensions, and can be lifted off shell too. In d
dimensions, the link between linearized gravity and its dual can also be seen
from the point of view of a parental action. This is defined by a first order
Lagrangian (with the help of some auxiliary variables) that delivers both
Fierz-Pauli theory and its dual. In this work we use this formalism to
implement the electric-magnetic duality in the nonrelativistic deviation of
Fierz-Pauli theory arising from Ho\v{r}ava-Lifshitz gravity. Because this
theory breaks diffeomorphism invariance, one finds that such implementation
includes some peculiarities.Comment: v1: 23 pages, 4 figures, edited with LaTeXila 2.4.0 and wxMaxima
12.04.0 for the graphics (Maxima version: 5.27.0). arXiv admin note: text
overlap with arXiv:1306.1092 by other authors; v2: 24 pages, 4 figures,
references added, negligence (leading to poor version management and
miscommunication) rectified; v3: typos and grammar corrected, minor changes
to uniformize convention