Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying Approach

Abstract

We provide a concise approach to generalized dilaton theories with and without torsion and coupling to Yang-Mills fields. Transformations on the space of fields are used to trivialize the field equations locally. In this way their solution becomes accessible within a few lines of calculation only. In this first of a series of papers we set the stage for a thorough global investigation of classical and quantum aspects of more or less all available 2D gravity-Yang-Mills models.

24 pages, no figures, some sign errors in Eqs. 52--59 have been corrected (according to the Erratum)

References in corpus (27)

• Geometrodynamics of Schwarzschild Black Holes
• Two-Dimensional Gravity and Nonlinear Gauge Theory
• Poisson Structure Induced (Topological) Field Theories
• The Statistical Mechanics of the (2+1)-Dimensional Black Hole
• Aspects of Black Hole Quantum Mechanics and Thermodynamics in 2+1 Dimensions
• Exact Dirac Quantization of All 2-D Dilaton Gravity Theories
• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• Spherically Symmetric Gravity as a Completely Integrable System
• String Model with Dynamical Geometry and Torsion
• Physical States in Matter-Coupled Dilaton Gravity
• TWO DIMENSIONAL DILATON GRAVITY COUPLED TO AN ABELIAN GAUGE FIELD
• The Black Holes of a General Two-Dimensional Dilaton Gravity Theory
• The Topological G/G WZW Model in the Generalized Momentum Representation
• Covariant Effective Action and One-Loop Renormalization of 2D Dilaton Gravity with Fermionic Matter
• Conserved Quasilocal Quantities and General Covariant Theories in Two Dimensions
• Dirac Quantization Gravity-Yang-Mills Systems in 1+1 Dimensions
• "Separation of Variables and Hamiltonian Formulation for the Ernst Equation"
• Diffeomorphisms Versus Non Abelian Gauge Transformations: An Example of 1+1 Dimensional Gravity
• Thermodynamics of Two Dimensional Black Holes
• On Induced Gravity in 2-d Topological Theories
• Two-dimensional higher-derivative gravity and conformal transformations
• The Quest for Quantum Gravity
• A Comparison of Two Quantization Procedures for Lineal Gravity
• Quantization of the Reduced Phase Space of Two-Dimensional Dilaton Gravity
• Quantum Coherence in Two Dimensions
• Quantization and the Issue of Time for Various Two-Dimensional Models of Gravity
• Quantal Modifications to the Wheeler DeWitt Equation

Cited by in corpus (93)

• Dilaton Gravity in Two Dimensions
• Quantum dilatonic gravity in d = 2,4 and 5 dimensions
• Non-existence of a dilaton gravity action for the exact string black hole
• Thermodynamics of Black Holes in Two (and Higher) Dimensions
• On the Completeness of the Black Hole Singularity in 2d Dilaton Theories
• Classical and Quantum Gravity in 1+1 Dimensions, Part II: The Universal Coverings
• The Classical Solutions of the Dimensionally Reduced Gravitational Chern-Simons Theory
• Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries
• Geometric Interpretation and Classification of Global Solutions in Generalized Dilaton Gravity
• Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse
• Tensor-multi-scalar theories from multidimensional cosmology
• Classical and Quantum Gravity in 1+1 Dimensions, Part III: Solutions of Arbitrary Topology
• Conservation and Integrability in Lower-Dimensional Gravity
• Algebroid Yang-Mills Theories
• Dirac Sigma Models
• Global properties of warped solutions in General Relativity
• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• Hamiltonian Thermodynamics of Black Holes in Generic 2-D Dilaton Gravity
• Integrating Geometry in General 2D Dilaton Gravity with Matter
• Geometrodynamical Formulation of Two-Dimensional Dilaton Gravity
• AdS_2 Supergravity and Superconformal Quantum Mechanics
• Effective action and Hawking radiation for dilaton coupled scalars in two dimensions
• S-matrix for s-wave gravitational scattering
• Open strings, 2D gravity and AdS/CFT correspondence
• Positive specific heat of the quantum corrected dilaton black hole
• Two-dimensional black holes as open strings: A new realization of the ADS/CFT correspondence
• Hawking radiation and masses in generalized dilaton theories
• Gravity from Lie algebroid morphisms
• Quantum-Corrected Cardy Entropy for Generic 1+1-Dimensional Gravity
• Nonperturbative path integral of 2d dilaton gravity and two-loop effects from scalar matter
• Free differential algebras and generic 2D dilatonic (super)gravities
• The classical solutions of two-dimensional gravity
• Generalized 2d dilaton gravity with matter fields
• The Complete Solution of 2D Superfield Supergravity from graded Poisson-Sigma Models and the Super Pointparticle
• Ramifications of Lineland
• Hamiltonian BRST deformation of a class of n-dimensional BF-type theories
• Gravitation with superposed Gauss--Bonnet terms in higher dimensions: Black hole metrics and maximal extensions
• A Global View of Kinks in 1+1 Gravity
• Supersymmetric black holes in 2D dilaton supergravity: baldness and extremality
• Absolute conservation law for black holes
• Edge States and Entropy of 2d Black Holes
• Universal conservation law and modified Noether symmetry in 2d models of gravity with matter
• Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution
• Dirac Sigma Models from Gauging
• Explicit Global Coordinates for Schwarzschild and Reissner-Nordstroem
• Effective action for scalar fields in two-dimensional gravity
• The Volume of 2D Black Holes
• Long time black hole evaporation with bounded Hawking flux
• Boundary Conditions and Quasilocal Energy in the Canonical Formulation of All 1+1 Models of Gravity
• New variables for 1+1 dimensional gravity
• Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space
• Quantum cosmology in the models of 2d and 4d dilatonic supergravity with WZ matter
• Two-Dilaton Theories in Two Dimensions from Dimensional Reduction
• Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model
• Virtual black hole phenomenology from 2d dilaton theories
• Consistent interactions of dual linearized gravity in D=5: couplings with a topological BF model
• Quantum gravity corrections to the Schwarzschild mass
• A Solvable Model of Two-Dimensional Dilaton-Gravity Coupled to a Massless Scalar Field
• PT-symmetry breaking hamiltonian interactions in BF models
• On static solutions in 2D dilaton gravity with scalar matter
• Two-dimensional gravity with an invariant energy scale
• dS${}_2$ as excitation of AdS${}_2$
• Quantum-Corrected Entropy for 1+1-Dimensional Gravity Revisited
• Flat space cosmologies in two dimensions - Phase transitions and asymptotic mass-domination
• Classical Solutions for Poisson Sigma Models on a Riemann surface
• Two-Dimensional Dilaton-Gravity Coupled to Massless Spinors
• Trace anomaly induced effective action and 2d black holes for dilaton coupled supersymmetric theories
• Two-dimensional metric-affine gravity
• Two-dimensional black holes in accelerated frames: Spacetime structure
• The Spherically Symmetric Standard Model with Gravity
• Physics-to-gauge conversion at black hole horizons
• Four-dimensional couplings among BF and massless Rarita-Schwinger theories: a BRST cohomological approach
• Self-interactions in a topological BF-type model in D=5
• Dynamical N-body Equlibrium in Circular Dilaton Gravity
• Couplings between a collection of BF models and a set of three-form gauge fields
• On the generalized Freedman-Townsend model
• Regular self-consistent geometries with infinite quantum backreaction in 2D dilaton gravity and black hole thermodynamics: unfamiliar features of familiar models
• The ultrarelativistic limit of 2D dilaton gravity and its energy momentum tensor
• 2d quantum dilaton gravity as/versus finite dimensional quantum mechanical systems
• Generalized dilaton gravity in 2d
• Exactly solvable models in 2D semiclassical dilaton gravity and extremal black holes
• Deformations of the Schwarzschild Black Hole
• Poisson-sigma model for 2D gravity with non-metricity
• Generalized Supergravity in Two Dimensions
• Two-Dimensional N=(2,2) Dilaton Supergravity from Graded Poisson-Sigma Models II: Analytic Solution and BPS States
• One-Dimensional Relativistic Self-Gravitating Systems
• Dynamical Charged N-body Equilibrium in Circular Dilaton Gravity
• The fate of Schwarzschild--de Sitter black holes: nonequilibrium evaporation
• The partition function of the linear Poisson-sigma model on arbitrary surfaces
• Solutions of arbitrary topology in 1+1 gravity
• Super Liouville Black Holes
• A note on dilaton gravity with non-smooth potentials
• The fate of Reissner--Nordström--de Sitter black holes: nonequilibrium discharge and evaporation