The evolution equations of the vorticities of the electrons, ions and photons
in a pre-decoupling plasma are derived, in a fully inhomogeneous geometry, by
combining the general relativistic gradient expansion and the drift
approximation within the Adler-Misner-Deser decomposition. The vorticity
transfer between the different species is discussed in this novel framework and
a set of general conservation laws, connecting the vorticities of the
three-component plasma with the magnetic field intensity, is derived. After
demonstrating that a source of large-scale vorticity resides in the spatial
gradients of the geometry and of the electromagnetic sources, the total
vorticity is estimated to lowest order in the spatial gradients and by
enforcing the validity of the momentum constraint. By acknowledging the current
bounds on the tensor to scalar ratio in the (minimal) tensor extension of the
ΞCDM paradigm the maximal comoving magnetic field induced by the total
vorticity turns out to be, at most, of the order of 10β37 G over the
typical comoving scales ranging between 1 and 10 Mpc. While the obtained
results seem to be irrelevant for seeding a reasonable galactic dynamo action,
they demonstrate how the proposed fully inhomogeneous treatment can be used for
the systematic scrutiny of pre-decoupling plasmas beyond the conventional
perturbative expansions.Comment: 36 page