Carrollian manifolds and null infinity: A view from Cartan geometry

Abstract

We discuss three different (conformally) Carrollian geometries and their relation to null infinity from the unifying perspective of Cartan geometry. Null infinity \emph{per se} comes with numerous redundancies in its intrinsic geometry and the two other Carrollian geometries can be recovered by making successive choices of gauge. This clarifies the extent to which one can think of null infinity as being a (strongly) Carrollian geometry and we investigate the implications for the corresponding Cartan geometries. The perspective taken, which is that characteristic data for gravity at null infinity are equivalent to a Cartan geometry for the Poincaré group, gives a precise geometrical content to the fundamental fact that ``gravitational radiation is the obstruction to having the Poincaré group as asymptotic symmetries''.

27 pages + refs, 1 figure, 4 tables summarizing results. This version coïncides with the published version. As suggested by the reviewers, the article is not presented as a review anymore to emphasise the original material

References in corpus (29)

• Asymptotic symmetries and subleading soft graviton theorem
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Carroll contractions of Lorentz-invariant theories
• Conformal Carroll groups
• Dynamics of Carroll Particles
• The Weyl BMS group and Einstein's equations
• Field Theories with Conformal Carrollian Symmetry
• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• Carrollian and celestial spaces at infinity
• Brown-York charges at null boundaries
• Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• AdS Carroll Chern-Simons supergravity in 2+1 dimensions and its flat limit
• Conformal submanifold geometry I-III
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• Planar Carrollean dynamics, and the Carroll quantum equation
• Near-horizon Carroll symmetry and black hole Love numbers
• Carroll limit of four-dimensional gravity theories in the first order formalism
• Tractor geometry of asymptotically flat spacetimes
• N-extended Chern-Simons Carrollian supergravities in 2+1 spacetime dimensions
• Scalar Fields in 3D Asymptotically Flat Higher-Spin Gravity
• BMS Field Theories and Weyl Anomaly
• The Generalized Good Cut Equation
• The Ashtekar-Hansen universal structure at spatial infinity is weakly pseudo-Carrollian
• A new look at the Bondi-Sachs energy-momentum
• A novel supersymmetric extension of BMS symmetries at null infinity
• Einstein gravity as a gauge theory for the conformal group

Cited by in corpus (24)

• Bridging Carrollian and Celestial Holography
• Holographic Lorentz and Carroll Frames
• Flat from anti-de Sitter
• Massless Scalars and Higher-Spin BMS in Any Dimension
• Graviton scattering in self-dual radiative space-times
• Carrollian conformal scalar as flat-space singleton
• Memory effects from holonomies
• Carroll Hawking effect
• Chern-Simons action and the Carrollian Cotton tensors
• Carrollian limit of quadratic gravity
• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• Quantization of Carrollian fermions
• Setting the connection free in the Galilei and Carroll expansions of gravity
• Supersymmetric Carroll Galileons in Three Dimensions
• Carroll-Schrödinger Equation
• Asymptotic symmetries of projectively compact order one Einstein manifolds
• Carroll black holes in (A)dS and their higher-derivative modifications
• One-dimensional Carrollian fluids I: Carroll-Galilei duality
• One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^{\infty }$
• Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds
• Unique Carrollian manifolds emerging from Einstein spacetimes
• Ti and Spi, Carrollian extended boundaries at timelike and spatial infinity
• Scaling Symmetry and Carrollian Gravity
• One-dimensional Carrollian fluids II: $C^1$ blow-up criteria