| dc.description |
We consider spacetimes which are asymptotically flat at spacelike infinity, . It is well known that, in general, one cannot have a smooth differentiable structure at , but rather one has to use direction-dependent structures there. Instead of the usual -differentiable structure, we suggest a weaker differential structure, a structure. The reason for this is that there do not appear to be any completions of the Schwarzschild spacetime which is in both spacelike and null directions at . In a structure all directions can be treated on an equal footing, at the expense of logarithmic singularities at . We show that, in general, the relevant part of the curvature tensor, the Weyl part, is free from these singularities, and that the (rescaled) Weyl tensor has a certain symmetry property. |
