Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe

Abstract

In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)-dimensional vacuum gravity in the setting of a spatially closed universe.

61 pages, draft of review for Living Reviews; comments, criticisms, additions, missing references welcome; v2: minor changes, added references

References in corpus (6)

• Introduction to Doubly Special Relativity
• Background independence in a nutshell
• Consistent discretization and loop quantum geometry
• 6j symbols for U_q(sl_2) and non-Euclidean tetrahedra
• 3D Lorentzian Quantum Gravity from the asymmetric ABAB matrix model
• Perturbation theory in covariant canonical quantization

Cited by in corpus (76)

• Quantum Spacetime Phenomenology
• Three-Dimensional Gravity Revisited
• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Cosmological Topologically Massive Gravitons and Photons
• Solving 3d Gravity with Virasoro TQFT
• Dynamics of Asymptotic Diffeomorphisms in (2+1)-Dimensional Gravity
• Reconstructing AdS/CFT
• On the steady states of the spherically symmetric Einstein-Vlasov system
• Classical and Quantum Correlations of Scalar Field in the Inflationary Universe
• One-loop renormalization in a toy model of Horava-Lifshitz gravity
• A Prehistory of n-Categorical Physics
• Black Hole Thermodynamics and Statistical Mechanics
• Dirac's discrete hypersurface deformation algebras
• Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Generic AdS3 Black Holes
• Split Quaternions and Particles in (2+1)-Space
• Geometrical (2+1)-gravity and the Chern-Simons formulation: Grafting, Dehn twists, Wilson loop observables and the cosmological constant
• Thermodynamical properties of an ideal gas in a traversable wormhole
• Hawking Radiation of Massive Vector Particles From Warped AdS${}_3$ Black Hole
• Noncommutative Geometries and Gravity
• Symmetries of topological gravity with torsion in the hamiltonian and lagrangian formalisms
• Stable three-dimensional (un)charged AdS gravastars in gravity's rainbow
• Maximally $\mathcal{N}$-extended super-BMS${}_3$ algebras and Generalized 3D Gravity Solutions
• Exact radial solution in 2+1 gravity with a real scalar field
• Synthetic Flux Attachment
• Thin shells in (2+1)-dimensional F(R) gravity
• Black Hole Entropy and the Problem of Universality
• A $T\bar{T}$ Deformation for Curved Spacetimes from 3d Gravity
• Hamiltonian formulation of tetrad gravity: three dimensional case
• Simulation of Acoustic Black Hole in a Laval Nozzle
• Horizons, Constraints, and Black Hole Entropy
• Bands and gaps in Nekrasov partition function
• Integrable Systems and Spacetime Dynamics
• (Curvature)^2-Terms for Supergravity in Three Dimension
• Cosmological measurements, time and observables in (2+1)-dimensional gravity
• Towards (3+1) gravity through Drinfel'd doubles with cosmological constant
• Black Hole Entropy and the Problem of Universality
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• Exploring Torus Universes in Causal Dynamical Triangulations
• Gauss-Bonnet black holes in (2+1) dimensions: Perturbative aspects and entropy features
• 3D gravity with propagating torsion: Hamiltonian structure of the scalar sector
• Shape Dynamics and Effective Field Theory
• On the self-consistency of compact objects in Lorentz-violating gravity theories
• Holographic Hierarchy in the Gaussian Matrix Model via the Fuzzy Sphere
• Can we see gravitational collapse in (quantum) gravity perturbation theory?
• Non-existence of Asymptotically Flat Geons in 2+1 Gravity
• Einstein-Maxwell gravity coupled to a scalar field in 2+1-dimensions
• Shape Dynamics in 2+1 Dimensions
• Thin-shell wormholes in (2+1)-dimensional F(R) theories
• Massive graviton propagation of the deformed Hořava-Lifshitz gravity without projectability condition
• Horizon Mechanics and Asymptotic Symmetries with a Immirzi-like Parameter in 2+1 Dimensions
• Nonexistence of marginally trapped surfaces and geons in 2+1 gravity
• Loop quantum cosmology in 2+1 dimension
• Black holes from multiplets of scalar fields in 2+1- and 3+1-dimensions
• Towards Canonical Quantum Gravity for G1 Geometries in 2+1 Dimensions with a Lambda--Term
• In Search of Fundamental Discreteness in 2+1 Dimensional Quantum Gravity
• Structure of $3D$ gravastars in the context of massive gravity
• D-dimensional self-gravitating lattice gas in general relativity
• On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity
• Holography for bulk states in 3D quantum gravity
• The (2+1)-dim Axial Universes -- Solutions to the Einstein Equations, Dimensional Reduction Points, and Klein-Fock-Gordon Waves
• Polynomial affine model of gravity in three-dimensions
• Gravitational interpretation of the Hitchin equations
• Hamiltonian solutions of the 3-body problem in (2+1)-gravity
• Thin-shell wormholes in 2+1-dimensional Einstein-Scalar Theory
• Generalized forms and gravitation
• Global Monopole metric in 2+1-dimensions
• Expanding and Self-Organizing 2D Universe Models Emerging from Frozen Trivalent Spin Networks
• Notes on solution phase space and BTZ black hole
• Thermodynamical and dynamical stability of Einstein-Maxwell and extremal Einstein-Born-Infeld thin shells in $(2+1)$ dimensions
• Beyond Operator Systems
• (2+1)-dimensional interacting model of two massless spin-2 fields as a bi-gravity model
• Topological Order of Quantum Gravity in $Ad{S}_3$ Spacetime
• 2+1 dimensional loop quantum cosmology of Bianchi I models
• Effects of curvature and gravity from flat spacetime
• Three-dimensional gravity and deformations of relativistic symmetries
• Generalized Chern-Simons action principles for gravity