The teleparallel equivalent of general relativity

Abstract

A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary observers in space-time is discussed, and the tensor of inertial accelerations on frames is obtained. It is shown that the Lagrangian and Hamiltonian field equations allow to define the energy, momentum and angular momentum of the gravitational field, as surface integrals of the field quantities. In the phase space of the theory, these quantities satisfy the algebra of the Poincaré group.

41 pages, 1 figure, published by the Annalen der Physik

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Cited by in corpus (361)

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• Observational Tests of Nonlocal Gravity: Galaxy Rotation Curves and Clusters of Galaxies
• Astrophysical flows near $f(T)$ gravity black holes
• Constraining f(T) gravity in the Solar System
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• Model-independent reconstruction of $f(T)$ teleparallel cosmology
• Solar System Tests in Modified Teleparallel Gravity
• Scalar-torsion theories of gravity III: analogue of scalar-tensor gravity and conformal invariants
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• Gravitoelectromagnetism, Solar System Test and Weak-Field Solutions in $f(T,B)$ Gravity with Observational Constraints
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• Metric-affine Geometries With Spherical Symmetry
• Reconstruction, Thermodynamics and Stability of $\Lambda$CDM Model in $f(T,\mathcal{T})$ Gravity
• Scalar-torsion theories of gravity I: general formalism and conformal transformations
• FRW in quadratic form of $f(T)$ gravitational theories
• Scalar-torsion theories of gravity II: $L(T,X,Y,\varphi )$ theory
• The gravitational energy-momentum pseudotensor: the cases of $f(R)$ and $f(T)$ gravity
• Generalized teleparallel cosmology and initial singularity crossing
• The Hidden Flat Like Universe: Starobinsky-like inflation induced by f(T) gravity
• Constraining $f(T,\mathcal{T})$ gravity models using type Ia supernovae
• $D$-dimensional charged Anti-de-Sitter black holes in $f(T)$ gravity
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• Charged Black Holes in Generalized Teleparallel Gravity
• The effective field theory approach to the strong coupling issue in $f(T)$ gravity
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• Analyzing the geometrical and dynamical parameters of modified Teleparallel-Gauss-Bonnet model
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• Modified teleparallel gravity with higher-derivative torsion terms
• McVittie solution in f(T) gravity
• Modified gravity: a unified approach to metric-affine models
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• Constraining $f(T,\mathcal{T})$ Gravity with Gravitational Baryogenesis
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• General cosmological perturbations in teleparallel gravity
• Realistic neutron star models in $f(T)$ gravity
• Rotating and non-rotating AdS black holes in $f(\mathcal{T})$ gravity non-linear electrodynamics
• Gravitationally Induced Particle Production through a Nonminimal Torsion-Matter Coupling
• Post-Newtonian limit of generalized scalar-torsion theories of gravity
• On the Viability of the Intermediate Inflation Scenario with $F(T)$ Gravity
• Premetric teleparallel theory of gravity and its local and linear constitutive law
• Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
• Gravitational Waves in Higher Order Teleparallel Gravity
• New cosmological constraints on $f(T)$ gravity in light of full Planck-CMB and type Ia supernovae data
• Nonmetricity theories and aspects of gauge symmetry
• Construction of spaces of kinematic quantum states for field theories via projective techniques
• An axiomatic purification of gravity
• On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity
• Dynamical system analysis of Myrzakulov gravity
• Exact Cosmology in Myrzakulov Gravity
• Unified dark sectors in scalar-torsion theories of gravity
• Spin Precession in Inertial and Gravitational Fields
• Mapping the ${\Lambda }_{\mathrm{s}}$CDM scenario to $f(T)$ modified gravity: Effects on structure growth rate
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry
• Primordial black holes and gravitational waves in teleparallel Gravity
• Flat connection for rotating vacuum spacetimes in extended teleparallel gravity theories
• Nonminimally coupled scalar field in teleparallel gravity: boson stars
• Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity
• Difficulties of Teleparallel Theories of Gravity with Local Lorentz Symmetry
• Kinematic quantum states for the Teleparallel Equivalent of General Relativity
• Lorentz symmetries and primary constraints in covariant teleparallel gravity
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• Viscous cosmology in $f(T)$ gravity
• A class of ghost-free theories in symmetric teleparallel geometry
• Teleparallel Newton--Cartan gravity
• Weitzenböck's Torsion, Fermi Coordinates and Adapted Frames
• Spontaneous Scalarization of Black Holes in Gauss-Bonnet Teleparallel Gravity
• The Stability of Anisotropic Compact Stars Influenced by Dark Matter under Teleparallel Gravity: An Extended Gravitational Deformation Approach
• Spherical Accretion of Matter by Charged Black Holes on f(T) Gravity
• Teleparallel gravity
• The energy-momentum tensor of gravitational waves, Wyman spacetime and freely falling observers
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• Transit cosmological models in Myrzakulov F(R,T) gravity theory
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• Conformally invariant proper time with general non-metricity
• Interaction of divergence-free deceleration parameter in Weyl-type $f(Q,T)$ gravity
• Black Holes, Dark Wormholes and Solitons in f(T) Gravities
• Testing MOG, Non-Local Gravity and MOND with rotation curves of dwarf galaxies
• Light bending in $f(T)$ gravity
• Noether gauge symmetry approach in quintom cosmology
• Solar system tests for realistic $f(T)$ models with nonminimal torsion-matter coupling
• Gravitational wave birefringence in spatially curved teleparallel cosmology
• A Complete Cosmological Scenario in Teleparallel Gravity
• Nonminimally coupled Weyl gravity
• Quintessence-like features in the late-time cosmological evolution of $f(Q)$ symmetric teleparallel gravity
• Scattering of Fermions by Gravitons
• Deflection angle, quasinormal modes and optical properties of a de Sitter black hole in $f(\mathcal{T},\mathcal{B})$ gravity
• Asymptotic cosmological regimes in scalar-torsion gravity with a perfect fluid
• Can $f(R)$ gravity isotropize a pre-bounce contracting universe?
• The Hidden Flat Like Universe II: Quasi inverse power law inflation by $f(T)$ gravity
• Geometrical Trinity of Unimodular Gravity
• Minisuperspace Quantum Cosmology in Metric and Affine Theories of Gravity
• The Teleparallel Equivalent of General Relativity and the Gravitational Centre of Mass
• Plane Gravitational Waves, the Kinetic Energy of Free Particles and the Memory Effect
• Charged Anti-de Sitter BTZ black holes in Maxwell-$f(T)$ gravity
• Localization of abelian gauge fields with Stueckelberg-like geometrical coupling on $f(T,B)$-thick brane
• Braneworlds in $f(Q)$ gravity
• Observational Constraints and Cosmographic Analysis of $f(T,T_G)$ Gravity and Cosmology
• Conformal Teleparallel Theories and Weyl Geometry
• $f(T)$ cosmology: From Pseudo-Bang to Pseudo-Rip
• Constraints on Power Law and Exponential models in $f(Q)$ Gravity
• Classification of primary constraints for new general relativity in the premetric approach
• Generic Phase Portrait Analysis of the Finite-time Singularities and Generalized Teleparallel Gravity
• Hyperscaling violating black holes in scalar-torsion theories
• Prospects of constraining $f(T)$ gravity with the third-generation gravitational-wave detectors
• Towards realistic $f(T)$ models with nonminimal torsion-matter coupling extension
• Repulsive gravity near naked singularities and point massive particles
• Irregular universe in the Nieh-Yan modified teleparallel gravity
• Exploring cosmological evolution and constraints in $f(T)$ teleparallel gravity
• General Teleparallel Modifications of Schwarzschild Geometry
• Cosmological study of a symmetric teleparallel gravity model
• The amplification of cosmological magnetic fields in Extended $f(T,B)$ Teleparallel Gravity
• Squared torsion $f(T,\mathcal{T})$ gravity and its cosmological implications
• On existence of a possible Lorentz invariant modified gravity in Weitzenböck spacetime
• A geometric view on local Lorentz transformations in teleparallel gravity
• Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
• Note on the charged boson stars with torsion-coupled field
• On Gravitational Energy in Conformal Teleparallel Gravity
• Maxwell-$f(Q)$ theory
• Observation constraints on scalar field cosmological model in Anisotropic universe
• Dynamical features of $f(T,B)$ cosmology
• Complete complementarity relations in curved spacetimes
• Slow-roll inflation in $f(T,\mathcal{T})$ modified gravity
• Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime
• $f(Q,T)$ gravity: From early to late-time cosmic acceleration
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• Renyi Holographic Dark Energy models in Teleparallel gravity
• Modified Teleparallel Gravity induced by quantum fluctuations
• f(T) Quantum Cosmology
• Einstein-Cartan-Dirac gravity with $U(1)$ symmetry breaking
• Variational Problem and Bigravity Nature of Modified Teleparallel Theories
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity II
• Bulk viscous fluid in symmetric teleparallel cosmology: theory versus experiment
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity I
• Spherical collapse and virialization in $f(T)$ gravities
• Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity
• New proper tetrad for teleparallel gravities in non-flat spacetime
• Energy Constraints and $F(T,T_G)$ Cosmology
• Spatially covariant gravity with nonmetricity
• Transferring Energy in General Relativity
• Thermodynamics in a Modified Gravity Involving Higher-Order Torsion Derivative Terms
• Phantom-Like Behavior in Modified Teleparallel Gravity
• The angular momentum of plane-fronted gravitational waves in the teleparallel equivalent of general relativity
• Dark energy as a kinematic effect
• The Work-Energy Relation for Particles on Geodesics in the pp-Wave Spacetimes
• Dynamical stability of extended teleparallel gravity
• Reconstructions of $f(\mathcal{P})$ and $f(\mathcal{Q})$ gravity models from $(m,n)$-type Barrow Holographic Dark Energy: Analysis and Observational Constraints
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Perturbation Spectra of Warm Inflation in $f(Q,T)$ Gravity
• Galaxy-galaxy lensing data: $f(T)$ gravity challenges General Relativity
• Effects of the matter Lagrangian degeneracy in $f(Q,T)$ gravity
• Teleparallel bigravity
• Gravitational energy, gravitational pressure, and the thermodynamics of a charged black hole in teleparallel gravity
• Generalized Teleparallel Theory
• From fundamental physics to tests with compact objects in metric-affine theories of gravity
• Reconstruction of $f(T,\mathcal{T})$ Lagrangian for various cosmological scenarios
• Quadratic and cubic spherically symmetric black holes in the modified teleparallel equivalent of general relativity: Energy and thermodynamics
• The generalization of the ADM gravitational energy-momentum
• Dual 2+1D Loop Quantum Gravity on the Edge
• Bondi-Sachs energy-momentum and the energy of gravitational radiation
• Dynamics of a higher-dimension Einstein-Scalar-Gauss-Bonnet cosmology
• Testing $f(T)$ Gravity with Cosmological Observations: Confronting the Hubble Tension and Implications for the Late-Time Universe
• Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions
• Anisotropic Cosmology in the Local Limit of Nonlocal Gravity
• Non-linear Plane Gravitational Waves as Space-time Defects
• Magnetic black holes in Weitzenböck geometry
• Gravitational energy and radiation of a charged black hole
• Teleparallel Geometry with Spherical Symmetry: The diagonal and proper frames
• Cosmological implications of non-minimally coupled f(Q) gravity
• The classification of general affine connections in Newton--Cartan geometry: Towards metric-affine Newton--Cartan gravity
• On the gravitational energy problem and the energy of photons
• Constraining some $r^{-n}$ extra-potentials in modified gravity models with LAGEOS-type laser-ranged geodetic satellites
• Background-dependent and classical correspondences between $f(Q)$ and $f(T)$ gravity
• Comparing measures of the Hubble and BAO tensions in $\Lambda$CDM and possible solutions in $f(Q)$ gravity
• $f(T)$ Gravity: Background Dependence and Propagating Degrees of Freedom
• Kinematics in Metric-Affine Geometry
• Perturbations of the Gravitational Energy in the TEGR: Quasinormal Modes of the Schwarzschild Black Hole
• Energy-momentum and angular-momentum of a gyratonic pp-waves spacetime
• Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation
• Late-time power-law stages of cosmological evolution in teleparallel gravity with nonminimal coupling
• Field transformations and invariant quantities in scalar-teleparallel theories of gravity
• Black hole solutions surrounded by anisotropic fluid in f(T,T) gravity
• On the Quantization of Burgers Vector and Gravitational Energy in the Space-Time of a Conical Defect
• On Nanocones as a Gravitational Analog System
• The meaning of torsion in teleparallel theories
• Local Limit of Nonlocal Gravity: Cosmological Perturbations
• Propagating Gravitational Waves in Teleparallel Gauss-Bonnet Gravity
• Non-singular bouncing cosmology in $f(T,\mathcal{T})$ gravity with energy condition violations
• Chiral Gravitational Wave Background from Audible Axion via Nieh-Yan Term
• Nonlocal General Relativity
• Tangent space symmetries in general relativity and teleparallelism
• Local Limit of Nonlocal Gravity: A Teleparallel Extension of General Relativity
• The Hamiltonian constraint in the symmetric teleparallel equivalent of general relativity
• Energy of Gravitational Radiation and the Background Energy of the Space-Time
• About the (in)equivalence between holonomic versus non-holonomic theories of gravity
• $SU(\infty )$ Quantum Gravity and Cosmology
• Phase space structure of symmetric teleparallel theory of gravity
• Gauge invariant perturbations in teleparallel Horndeski gravity
• Role of the remnant symmetries in gravitational theories based on absolute parallelism: a 2D standpoint
• Compact stellar model in higher torsion gravitational theory
• D=11 cosmologies with teleparallel structure
• Action functional of the Cardassian universe
• Distinctive Features of Hairy Black Holes in Teleparallel Gauss-Bonnet Gravity
• Thick branes in Born-Infeld determinantal gravity in Weitzenböck spacetime
• Proposal for the proper gravitational energy-momentum tensor
• Degrees of Freedom of New General Relativity I: Type 2, Type 3, Type 5, and Type 8
• Mass and angular momentum for the Kerr black hole in TEGR and STEGR
• On the total energy conservation of the Alcubierre spacetime
• On the Black Hole Acceleration in the C-metric Space-time
• Teleparallelism as anholonomic geometry
• Rotating cosmological cylindrical wormholes in GR and TEGR sourced by anisotropic fluids
• On Quantum Cosmology in Teleparallel Gravity
• Distorted Torsion Tensor, Teleparallelism and Spin 2 Field Equations
• Localization of Energy-Momentum for a Black Hole Spacetime Geometry with Constant Topological Euler Density
• Gravitational Pressure and the Accelerating Universe
• A Universe from a Lagrangian Fixed Point
• Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry
• Charged Gravastar Solutions in the Finch-Skea Framework with f(\mathbb{Q}) Gravity
• Covariant Fractons and Weitzenböck Torsion
• Does the metric play a fundamental role in the building of gravitational models?
• Constraints of the Teleparallel Equivalent of General Relativity in a gauge
• Electroweak interaction beyond the Standard Model and Dark Matter in the Tangent Bundle Quantum Field Theory
• The irreducible mass of a regular rotating black hole
• Dynamics and gravitational radiation of binaries with spin precession and eccentricity in dynamical Chern-Simons gravity
• Singular teleparallelism
• On Fermion-Graviton Scattering at Finite Temperature
• On the Temperature of Gravitation in the de Sitter Space-Time
• Gauge invariant perturbations of $F(T,T_G)$ Cosmology
• Teleparallel Poincaré Cosmology and $\Lambda$CDM Model
• Cosmological Constraints on f(T,B) Gravity from Observations of Early and Late Universe
• On Regular Black Holes at Finite Temperature
• Gravitational Energy Creation in the Sandwich pp-Waves Collision
• Bayesian Inference of Neutron Star Properties in $f(Q)$ Gravity Using NICER Observations
• The Role of Gravitational Energy Flux in Cosmic Acceleration
• Quantum gravity: the Inverse problem
• On the Gravitational Angular Momentum of Axial Perturbations of a Regular Black Hole
• Conceptual and Geometric Foundations for a Teleparallel Approach to Quantum Gravity
• Quantum geometry from commutators: a Heisenberg-picture framework and a toy application to early structure
• Towards a unified theory of the fundamental physical interactions based on the underlying geometric structure of the tangent bundle
• Blueshift of light rays induced by gravitational wave memory effect
• Generators of Local Lorentz Transformation in ADM-Vielbein Formalism of Gravitational Relativity
• Bi-connected Gravity Fields
• Dynamics of Linear Scalar Perturbation in f(Q)+f(T) class of f(Q,T) gravity
• At the Corner of Space and Time
• Spin Networks and Cosmic Strings in 3+1 Dimensions
• A teleparallel type theory for massless spin 2 fields
• Gödel's Universe and the Local Limit of Nonlocal Gravity
• On Gravitational Stefan-Boltzmann Law and Casimir Effect in FRW Universe
• Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity
• Bulk-boundary decompositions and exact perfect fluid stellar distributions
• Gravitational energy in pp-wave spacetimes
• Cylindrically symmetric static $n$-dimensional (un)charged (anti-)de Sitter black holes in generic $f(T)$ gravity
• Inflation and primordial fluctuations in $f(Q,T)$ gravity
• Static plane symmetric solutions in $f(Q)$ gravity
• Dynamical systems approach to stellar modelling in $f(G,B)$ gravity