In the case of charges defined at space-like infinity, I can understand the physical meaning of them because they can be related to measurements made by a physical observer (that is an observer whose wordline is time-like). For example in four dimensions, for the Schwarschild solution, the ADM mass coincide with the mass measured by an observer that is motionless (in Schwarschild coordinates) and far from the center of the solution.
My puzzle is then the following : since no physical observer can reach light-like infinity, how are physically interpreted the charges defined at light-like infinity? How are they related to any measurement?
Many thanks for your help.