  We present a new set of asymptotic conditions for gravity at spatial infinity
that includes gravitational magnetic-type solutions, allows for a non-trivial
Hamiltonian action of the complete $BMS_4$ algebra, and leads to a
non-divergent behaviour of the Weyl tensor as one approaches null infinity. We
then extend the analysis to the coupled Einstein-Maxwell system and obtain as
canonically realized asymptotic symmetry algebra a semi-direct sum of the
$BMS_4$ algebra with the angle dependent $u(1)$ transformations. The
Hamiltonian charge-generator associated with each asymptotic symmetry element
is explicitly written. The connection with matching conditions at null infinity
is also discussed.
