Carroll Structures, Null Geometry and Conformal Isometries

Abstract

We study the concept of Carrollian spacetime starting from its underlying fiber-bundle structure. The latter admits an Ehresmann connection, which enables a natural separation of time and space, preserved by the subset of Carrollian diffeomorphisms. These allow for the definition of Carrollian tensors and the structure at hand provides the designated tools for describing the geometry of null hypersurfaces embedded in Lorentzian manifolds. Using these tools, we investigate the conformal isometries of general Carrollian spacetimes and their relationship with the BMS group.

arXiv commentv1: 15 pages, Latex

References in corpus (15)

• Aspects of the BMS/CFT correspondence
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• The BMS/GCA correspondence
• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Gauging the Carroll Algebra and Ultra-Relativistic Gravity
• Flat holography and Carrollian fluids
• Conformal Carroll groups
• Symmetries and charges of general relativity at null boundaries
• Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids
• Connections and dynamical trajectories in generalised Newton-Cartan gravity II. An ambient perspective
• Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view
• Gravity Degrees of Freedom on a Null Surface
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Cited by in corpus (105)

• Carrollian Perspective on Celestial Holography
• Carrollian Physics at the Black Hole Horizon
• Carroll contractions of Lorentz-invariant theories
• Bridging Carrollian and Celestial Holography
• Fractons, dipole symmetries and curved spacetime
• The Weyl BMS group and Einstein's equations
• Extended corner symmetry, charge bracket and Einstein's equations
• Carroll Expansion of General Relativity
• Isolated Surfaces and Symmetries of Gravity
• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• Conformal Carroll Scalars with Boosts
• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
• Brown-York charges at null boundaries
• Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations
• Carrollian hydrodynamics from symmetries
• Carrollian manifolds and null infinity: A view from Cartan geometry
• On the intrinsic torsion of spacetime structures
• Carroll black holes
• Universal Corner Symmetry and the Orbit Method for Gravity
• Carroll covariant scalar fields in two dimensions
• Planar Carrollean dynamics, and the Carroll quantum equation
• Non-linear black hole dynamics and Carrollian fluids
• Holographic Lorentz and Carroll Frames
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• Flat from anti-de Sitter
• BMS-like symmetries in cosmology
• Massless Scalars and Higher-Spin BMS in Any Dimension
• Constructing Carrollian CFTs
• Intrinsic Approach to $1+1$D Carrollian Conformal Field Theory
• Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
• The partial Bondi gauge: Gauge fixings and asymptotic charges
• Carroll limit of four-dimensional gravity theories in the first order formalism
• Non-Riemannian isometries from double field theory
• Scaling and conformal symmetries for plane gravitational waves
• Symmetry group at future null infinity I: Scalar theory
• Carrollian Origin of Spacetime Subsystem Symmetry
• Galilean first-order formulation for the non-relativistic expansion of general relativity
• Hydro & Thermo Dynamics at Causal Boundaries, Examples in 3d Gravity
• Tractor geometry of asymptotically flat spacetimes
• Galilean Gauge Theories from Null Reductions
• Quantum Null Geometry and Gravity
• Renormalization of conformal infinity as a stretched horizon
• Null Infinity as a Weakly Isolated Horizon
• Horizon Strings as 3d Black Hole Microstates
• On Symplectic Form for Null Boundary Phase Space
• Virasoro hair and entropy for axisymmetric Killing horizons
• Symmetry group at future null infinity II: Vector theory
• Carrollian Supersymmetry and SYK-like models
• Carrollian Yang-Mills Theory
• Ehlers, Carroll, Charges and Dual Charges
• Weyl-Ambient Geometries
• BMS Field Theories and Weyl Anomaly
• Hamiltonian form of `Carroll' gravity
• On the Various Extensions of the BMS Group
• Quantization of Carrollian conformal scalar theories
• Fluid-gravity correspondence and causal first-order relativistic viscous hydrodynamics
• Carroll Hawking effect
• Corner symmetry and quantum geometry
• Chern-Simons action and the Carrollian Cotton tensors
• Carrollian limit of quadratic gravity
• Flat Bands and Compact Localised States: A Carrollian roadmap
• Extended Kinematical 3D Gravity Theories
• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• Radiation in Fluid/Gravity and the Flat Limit
• A novel supersymmetric extension of BMS symmetries at null infinity
• Setting the connection free in the Galilei and Carroll expansions of gravity
• Asymptotic Limit of Null Hypersurfaces
• Quantum Area Fluctuations from Gravitational Phase Space
• Some useful operators on differential forms in Galilean and Carrollian spacetimes
• Quantum symmetries in 2+1 dimensions: Carroll, (a)dS-Carroll, Galilei and (a)dS-Galilei
• Carroll-Schrödinger Equation
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Looking for Carroll particles in two time spacetime
• Supersymmetric Carroll Galileons in Three Dimensions
• Field-dependent diffeomorphisms and the transformation of surface charges between gauges
• Fate of $\kappa$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes
• One-dimensional Carrollian fluids I: Carroll-Galilei duality
• Carroll black holes in (A)dS and their higher-derivative modifications
• Asymptotic symmetries in Carrollian theories of gravity
• On Super-Translation transition between Quasi-local Black holes
• One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^{\infty }$
• AdS${}_3$ Carroll gravity: asymptotic symmetries and C-thermal configurations
• Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars
• Galilean and Carrollian Hodge star operators
• Universal sectors of two-dimensional Carrollian CFTs
• Sourced Carrollian Fluids Dual to Black Hole Horizons
• Fefferman-Graham and Bondi Gauges in the Fluid/Gravity Correspondence
• Unique Carrollian manifolds emerging from Einstein spacetimes
• A twistorial description of BMS symmetries at null infinity
• Dynamical horizons and Super-Translation transitions of the horizon
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model
• Asymptotic symmetries in Carrollian theories of gravity with a negative cosmological constant
• Null Strings Gauged and Reloaded, I: Null Strings Have Carroll-Weyl Gauge Symmetry
• Using thermodynamics to learn gravitational wave physics
• Revisiting the Carrollian Scalar Field
• Null infinity as a Killing horizon
• One-dimensional Carrollian fluids II: $C^1$ blow-up criteria
• Carrollian ${\mathbb{R}}^{\times }$-bundles: Connections and Beyond
• Quantum fields on projective geometries
• On Carrollian and Galilean contractions of BMS algebra in 3 and 4 dimensions
• Lectures on the Bondi--Metzner--Sachs group and related topics in infrared physics
• Circularly polarized periodic gravitational wave and the Pais-Uhlenbeck oscillator
• Nonperfect Carrollian Fluids Through Holography