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''.

arXiv comment27 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 (71)

• Isolated and dynamical horizons and their applications
• Soft Hair on Black Holes
• On BMS Invariance of Gravitational Scattering
• Aspects of the BMS/CFT correspondence
• 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
• A 3+1 perspective on null hypersurfaces and isolated horizons
• Gauging the Carroll Algebra and Ultra-Relativistic Gravity
• Carrollian Physics at the Black Hole Horizon
• Carroll contractions of Lorentz-invariant theories
• Flat holography and Carrollian fluids
• Carroll Structures, Null Geometry and Conformal Isometries
• Conformal Carroll groups
• Carroll versus Galilei Gravity
• Dynamics of Carroll Particles
• Bondi-Sachs Formalism
• The $\Lambda$-BMS${}_4$ group of dS${}_4$ and new boundary conditions for AdS${}_4$
• The Weyl BMS group and Einstein's equations
• Field Theories with Conformal Carrollian Symmetry
• Symmetries and charges of general relativity at null boundaries
• MacDowell-Mansouri gravity and Cartan geometry
• Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids
• Perfect Fluids
• Finite BMS transformations
• BMS Supertranslations and Memory in Four and Higher Dimensions
• Null infinity, the BMS group and infrared issues
• Vacua of the gravitational field
• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• Carroll symmetry of plane gravitational waves
• Carrollian conservation laws and Ricci-flat gravity
• Field Theories on Null Manifolds
• Gravity Degrees of Freedom on a Null Surface
• Carrollian and celestial spaces at infinity
• Brown-York charges at null boundaries
• Two-dimensional fluids and their holographic duals
• Null Conservation Laws for Gravity
• Spatially isotropic homogeneous spacetimes
• Boundary effects in General Relativity with tetrad variables
• Non-Boost Invariant Fluid Dynamics
• Embedding Galilean and Carrollian geometries I. Gravitational waves
• Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Interacting Conformal Carrollian Theories: Cues from Electrodynamics
• AdS Carroll Chern-Simons supergravity in 2+1 dimensions and its flat limit
• Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension
• Conformal submanifold geometry I-III
• Planar Carrollean dynamics, and the Carroll quantum equation
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• The Effective Action of Superrotation Modes
• The Symmetries of the Carroll Superparticle
• On the geometry of impulsive gravitational waves
• Near-horizon Carroll symmetry and black hole Love numbers
• Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
• Carroll limit of four-dimensional gravity theories in the first order formalism
• VSUSY models with Carroll or Galilei invariance
• Tractor geometry of asymptotically flat spacetimes
• N-extended Chern-Simons Carrollian supergravities in 2+1 spacetime dimensions
• Lorentzian Snyder spacetimes and their Galilei and Carroll limits from projective geometry
• 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
• Kinematical superspaces
• 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