Cosmic footballs from superrotations

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.

arXiv comment24+8 pages, 8 figures

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Cited by in corpus (14)

• Generalized BMS charge algebra
• The Holographic Nature of Null Infinity
• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• A general framework for gravitational charges and holographic renormalization
• Goldilocks Modes and the Three Scattering Bases
• The Effective Action of Superrotation Modes
• General null asymptotics and superrotation-compatible configuration spaces in $d\ge 4$
• A Comment on Loop Corrections to the Celestial Stress Tensor
• Celestial Recursion
• Chaos in Celestial CFT
• Celestial IR divergences and the effective action of supertranslation modes
• Super-Hawking Radiation
• Entanglement Rényi entropies in celestial holography
• A Celestial Description of Planar Super-Yang-Mills Theory