  The asymptotic dynamics of AdS$_3$ gravity with two asymptotically anti-de
Sitter regions is investigated, paying due attention to the zero modes, i.e.,
holonomies along non-contractible circles and their canonically conjugates.
This situation covers the eternal black hole solution. We derive how the
holonomies around the non-contractible circles couple the fields on the two
different boundaries and show that their canonically conjugate variables,
needed for a consistent dynamical description of the holonomies, can be related
to Wilson lines joining the boundaries. The action reduces to the sum of four
free chiral actions, one for each boundary and each chirality, with additional
non-trivial couplings to the zero modes which are explicitly written. While the
Gauss decomposition of the $SL(2,\mathbb{R})$ group elements is useful in order
to treat hyperbolic holonomies, the Iwasawa decomposition turns out to be more
convenient in order to deal with elliptic and parabolic holonomies. The
connection with the geometric action is also made explicit. Although our paper
deals with the specific example of two asymptotically anti-de Sitter regions,
most of our global considerations on holonomies and radial Wilson lines
qualitatively apply whenever there are multiple boundaries, independently of
the form that the boundary conditions explicitly take there.
