Early radiative properties of the developments of time-symmetric conformally flat initial data

Using a representation of spatial infinity based on the properties of conformal geodesics, the first terms of an expansion for the Bondi mass for the development of time-symmetric, conformally flat initial data are calculated. As is to be expected, the Bondi mass agrees with the ADM at the sets where null infinity ʹtouchesʹ spatial infinity. The second term in the expansion is proportional to the sum of the squared norms of the Newman-Penrose constants of the spacetime. On the basis of this result it is argued that these constants may provide a measure of the incoming radiation contained in the spacetime. This is illustrated by means of the Misner and Brill-Lindquist datasets.