Logarithmic supertranslations and supertranslation-invariant Lorentz charges

We extend the BMS(4) group by adding logarithmic supertranslations. This is done relaxing boundary conditions on metric and its conjugate momentum at spatial infinity in order to allow terms of carefully designed form asymptotic expansion, while still preserving finiteness action. Standard theorems Hamiltonian formalism are used derive (finite) generators As ordinary supertranslations, these depend a function angles. Ordinary supertranslations then shown an abelian subalgebra with non-vanishing central extension. Because this term, one can make nonlinear redefinitions algebra so that pure ($\ell >1$ spherical harmonic expansion) have vanishing brackets all Poincar\'e generators, and, particular, transform trivial representation Lorentz group. The symmetry direct sum infinite-dimensional formed (with extension). thus completely decoupled from standard algebra. implies particular provide definition angular which manifestly free supertranslation ambiguities. An intermediate redefinition providing partial decoupling also given.