A comparison of Ashtekar's and Friedrich's formalisms of spatial infinity

Understand

Penrose's idea of asymptotic flatness provides a framework for understanding the asymptotic structure of gravitational fields of isolated systems at null infinity.

• However, the studies of the asymptotic behaviour of fields near spatial infinity are more challenging due to the singular nature of spatial infinity in a regular point compactification for spacetimes with non-vanishing ADM mass.
• Two different frameworks that address this challenge are Friedrich's cylinder at spatial infinity and Ashtekar's definition of asymptotically Minkowskian spacetimes at spatial infinity that give rise to the 3-dimensional asymptote at spatial infinity $\mathcal{H}$.
• Both frameworks address the singularity at spatial infinity although the link between the two approaches had not been investigated in the literature.