This paper investigates the possibility of eliminating the supertranslation gauge freedom at scri by the introduction of a unique set of sections, which may be understood as giving a centre of mass system of reference. The construction depends on the properties of the physical system at the fixed retarded time defined by these sections.

This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references in the literature where normally stringent assumptions are made on the sources. The new expressions are manifestly gauge invariant, since they are presented in terms of curvature components. We also present a method of approximation for solving the lens equations, that can be applied to any order.PACS numbers: 95.30.Sf

We revisit the calculation of gravitational radiation through the use of Weyl scalars. We point out several possible problems arising from gauge and tetrad ambiguities and ways to address them. Our analysis indicates how, relatively simple corrections can be introduced to remove these ambiguities.PACS numbers:

The standard notions of asymptotically flat spacetimes have been challenged by the examples found by Isaacson, Welling and Winicour (1984), which show logarithmic asymptotic behaviour. Here, a geometrical definition of general future asymptotically flat (GeFAF) spacetimes is introduced, and its implications are systematically studied throughout the paper. Conformal techniques are used, but no reference to field equations is made. In particular logarithmic behaviour is studied. For the general GeFAF case it is deduced that the radiation fields always behave like 1/r asymptotically.