Cosmic footballs from superrotations

TL;DR

This paper proposes an alternative way to understand superrotations in asymptotically flat spacetime, avoiding defects in the bulk by allowing boundary metric singularities, and explores their geometric and gauge properties.

Contribution

It introduces a new interpretation of superrotations as self-maps of Minkowski space, avoiding spacetime defects and analyzing their geometric and gauge implications.

Findings

Superrotations can be realized as multivalued or non-surjective maps of Minkowski space.

Superrotations preserve hyperbolic slicing in Newman-Unti gauge.

The new interpretation broadens the scope of celestial sphere metrics and asymptotic symmetries.

Abstract

Superrotations arise from singular vector fields on the celestial sphere in asymptotically flat space, and their finite integrated versions have been argued by Strominger and Zhiboedov to insert cosmic strings into the spacetime. In this work, we argue for an alternative definition of the action of superrotations on Minkowski space that avoids introducing any defects. This involves realizing the finite superrotation not as a diffeomorphism between spaces, but as a mapping of Minkowski space to itself that may be multivalued or non-surjective. This eliminates any defects in the bulk spacetime at the expense of allowing for defects in the boundary celestial sphere metric. We further explore the geometry of the spatial surfaces in the superrotated spaces, and note that they intersect null infinity at the singularity of the superrotation, causing a breakdown in the large $r$ asymptotic expansion there. To determine how these surfaces embed into Minkowski space, a derivation of the finite superrotation transformation is presented in both Bondi and Newman-Unti gauges. The latter is particularly interesting, since the superrotations are shown to preserve the hyperbolic slicing of Minkowski space in Newman-Unti gauge, and this gauge also provides a means for extending the geometry beyond the Bondi coordinate patch. We argue that the new interpretation for the action of superrotations on spacetime motivates consideration of a wider class of celestial sphere metrics and asymptotic symmetry groups.