On the differentiability conditions at spacelike infinity
Magnus Herberthson; Magnus Herberthson; Linköping University, Department of Mathematics, S-581 83 Linköping, Sweden
Журнал:
Classical and Quantum Gravity
Дата:
1998-12-01
Аннотация:
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.
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