  It is well known in the context of four dimensional asymptotically flat
spacetimes that the leading order boundary metric must be conformal to unit de
Sitter metric when hyperbolic cutoffs are used. This situation is very
different from asymptotically AdS settings where one is allowed to choose an
arbitrary boundary metric. The closest one can come to changing the boundary
metric in the asymptotically flat context, while maintaining the group of
asymptotic symmetries to be Poincare, is to change the so-called
`supertranslation frame' \omega. The most studied choice corresponds to taking
\omega = 0. In this paper we study consequences of making alternative choices.
We perform this analysis in the covariant phase space approach as well as in
the holographic renormalization approach. We show that all choices for \omega
are allowed in the sense that the covariant phase space is well defined
irrespective of how we choose to fix supertranslations. The on-shell action and
the leading order boundary stress tensor are insensitive to the
supertranslation frame. The next to leading order boundary stress tensor
depends on the supertranslation frame but only in a way that the transformation
of angular momentum under translations continues to hold as in special
relativity.
