  Four-dimensional asymptotically flat spacetimes at spatial infinity are
defined from first principles without imposing parity conditions or
restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a
correct variational principle when it is supplemented by an anomalous
counter-term which breaks asymptotic translation, supertranslation and
logarithmic translation invariance. Poincar\'e transformations as well as
supertranslations and logarithmic translations are associated with finite and
conserved charges which represent the asymptotic symmetry group. Lorentz
charges as well as logarithmic translations transform anomalously under a
change of regulator. Lorentz charges are generally non-linear functionals of
the asymptotic fields but reduce to well-known linear expressions when parity
conditions hold. We also define a covariant phase space of asymptotically flat
spacetimes with parity conditions but without restrictions on the Weyl tensor.
In this phase space, the anomaly plays classically no dynamical role.
Supertranslations are pure gauge and the asymptotic symmetry group is the
expected Poincar\'e group.
