  In arXiv:1904.12869 it was shown how in an adiabatic limit the vacuum
Einstein equations on a compact spatial region can be re-expressed as geodesic
equations on the group of diffeomorphisms of the boundary. This is reminiscent
of the program initiated by V. Arnold to reformulate models of continuum
mechanics in terms of geodesic motion on diffeomorphism groups. We revisit some
of the results of arXiv:1904.12869 in this light, pointing out parallels and
differences with the typical examples in geometric continuum mechanics. We work
out the case of 2 spatial dimensions in some detail.
