A C>1 Completion of the Kerr Space–Time at Spacelike Infinity Including I+ and I−

Abstract

It is well known that, for asymptotically flat spacetimes, one cannot in general have a smooth differentiable structure at spacelike infinity, i ⁰. Normally, one uses direction dependent structures, whose regularity has to match the regularity of the (rescaled) metric. The standard C ^>1-structure at i ⁰ ensures sufficient regularity in spacelike directions, but examples show very low regularity on I ⁺ and I ⁻. The alternative C ¹⁺-structure shows that both null and spacelike directions may be treated on an equal footing, at the expense of some manageable logarithmic singularities at i ⁰. In this paper, we show that the Kerr spacetime may be rescaled and given a structure which is C ^>1 in both null and spacelike directions from i ⁰.