On the covariance of teleparallel gravity theories

Abstract

The basics of teleparallel gravity and its extensions are reviewed with particular emphasis on the problem of Lorentz-breaking choice of connection in pure-tetrad versions of the theories. Various possible ways to covariantise such models are discussed. A by-product is a new form of $f(T)$ field equations.

14 pages; final version accepted by CQG

References in corpus (4)

• Einstein's Other Gravity and the Acceleration of the Universe
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Good and bad tetrads in f(T) gravity
• Remnant Symmetry, Propagation and Evolution in f(T) Gravity

Cited by in corpus (147)

• Teleparallel Gravity: From Theory to Cosmology
• $f(Q,T)$ gravity
• Coupling matter in modified $Q$-gravity
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Teleparallel Palatini theories
• Nonmetricity formulation of general relativity and its scalar-tensor extension
• Weyl type $f(Q,T)$ gravity, and its cosmological implications
• Covariant formulation of scalar-torsion gravity
• Cosmological perturbations in modified teleparallel gravity models
• New classes of modified teleparallel gravity models
• Noether symmetries in Symmetric Teleparallel Cosmology
• Modified teleparallel theories of gravity in symmetric spacetimes
• Polarization of gravitational waves in symmetric teleparallel theories of gravity and their modifications
• The spectrum of symmetric teleparallel gravity
• Hamiltonian formalism for f(T) gravity
• Stable and self-consistent compact star models in teleparallel gravity
• Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity
• Photon sphere and perihelion shift in weak $f(T)$ gravity
• Conformal Gravity and Transformations in the Symmetric Teleparallel Framework
• Scale transformations in metric-affine geometry
• Family of scalar-nonmetricity theories of gravity
• Anisotropic Strange Star Model Beyond Standard Maximum Mass Limit by Gravitational Decoupling in $f(Q)$ Gravity
• Stability of motion and thermodynamics in charged black holes in $f(T)$ gravity
• Teleparallel theories of gravity as analogue of non-linear electrodynamics
• Propagation of gravitational waves in teleparallel gravity theories
• Hamiltonian and primary constraints of new general relativity
• Gravitoelectromagnetism, Solar System Test and Weak-Field Solutions in $f(T,B)$ Gravity with Observational Constraints
• Foundational issues in f(T) gravity theory
• Scalar-torsion theories of gravity I: general formalism and conformal transformations
• Scalar-torsion theories of gravity II: $L(T,X,Y,\varphi )$ theory
• Quest for the extra degree of freedom in f(T) gravity
• Compact stars in $f(T)$ extended theory of gravity
• Review of the Hamiltonian analysis in teleparallel gravity
• Conformally symmetric traversable wormholes in modified teleparallel gravity
• On an integrable geometrical foundation of gravity
• Minkowski space in $f(T)$ gravity
• Coincident gauge for static spherical field configurations in symmetric teleparallel gravity
• Non-trivial Minkowski backgrounds in f(T) gravity
• Black hole solutions in the quadratic Weyl conformal geometric theory of gravity
• Dark matter as a Weyl geometric effect
• Static spherically symmetric black holes in weak f(T)-gravity
• On the gauge fixing in the Hamiltonian analysis of general teleparallel theories
• Bianchi identities in f(T) gravity: paving the way to confrontation with astrophysics
• Einstein-Cartan Cosmologies
• Nonlocal Teleparallel Cosmology
• The Teleparallel Equivalent of Newton-Cartan Gravity
• Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions
• Higgs inflation and teleparallel gravity
• Black hole solutions in scalar-tensor symmetric teleparallel gravity
• Deflection angle and lensing signature of covariant f(T) gravity
• Variational Principles in Teleparallel Gravity Theories
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• $H_0$ Tension and the Phantom Regime: A Case Study In Terms of an Infrared $f(T)$ Gravity
• Reflections on the covariance of modified teleparallel theories of gravity
• Parameterized post-Newtonian limit of general teleparallel gravity theories
• Transit cosmological models with observational constraints in f(Q, T) gravity
• Toward a concordance teleparallel Cosmology I: Background Dynamics
• Connection independent formulation of general relativity
• Coupling matter and curvature in Weyl geometry: conformally invariant $f\left(R,L_m\right)$ gravity
• Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term
• Exploring Axial Symmetry in Modified Teleparallel Gravity
• Continuum mechanics with torsion
• Dynamical complexity of the Teleparallel gravity cosmology
• Noether symmetries and boundary terms in extended Teleparallel gravity cosmology
• Modelling the Accelerating Universe with $f(Q)$ Gravity: Observational Consistency
• Teleparallel axions and cosmology
• Realistic neutron star models in $f(T)$ gravity
• Testing Born-Infeld $f(T)$ teleparallel gravity through Sgr A${}^{\star }$ observations
• Counting Components in the Lagrange Multiplier Formulation of Teleparallel Theories
• Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
• An axiomatic purification of gravity
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• Nonmetricity theories and aspects of gauge symmetry
• Symmetric Teleparallel Geometries
• On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity
• The regular black hole in four dimensional Born-Infeld gravity
• Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity
• Flat connection for rotating vacuum spacetimes in extended teleparallel gravity theories
• Lorentz symmetries and primary constraints in covariant teleparallel gravity
• Spontaneous Scalarization of Black Holes in Gauss-Bonnet Teleparallel Gravity
• Bounce Models within Teleparallel modified gravity
• Boson stars in $f(T)$ extended theory of gravity
• Geometry and covariance of symmetric teleparallel theories of gravity
• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
• Perturbations in f(T) cosmology and the spin connection
• Polarization of gravitational waves in general teleparallel theories of gravity
• The energy-momentum tensor of gravitational waves, Wyman spacetime and freely falling observers
• $f(Q,L_m)$ gravity, and its cosmological implications
• Spherically symmetric teleparallel geometries
• Disformal transformations in modified teleparallel gravity
• On spherically symmetric vacuum solutions and horizons in covariant $f(T)$ gravity theory
• Junction Conditions for F(T) Gravity from a Variational Principle
• Stability of symmetric teleparallel scalar-tensor cosmologies with alternative connections
• Unexplored regions in teleparallel $f(T)$ gravity: Sign-changing dark energy density
• Teleparallel Equivalent of Lovelock Gravity, Generalizations and Cosmological Applications
• Conformal Teleparallel Theories and Weyl Geometry
• The geometrical meaning of the Weitzenböck connection
• Dynamical Complexity in Teleparallel Gauss-Bonnet Gravity
• General Teleparallel Modifications of Schwarzschild Geometry
• Solving Tolman-Oppenheimer-Volkoff equations in $f(T)$ gravity: a novel approach
• Dynamic properties of cyclic cosmologies
• A geometric view on local Lorentz transformations in teleparallel gravity
• Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
• Variational Problem and Bigravity Nature of Modified Teleparallel Theories
• Hamilton's equations in the covariant teleparallel equivalent of general relativity
• f(T) Quantum Cosmology
• Static spherically symmetric solutions in New General Relativity
• New proper tetrad for teleparallel gravities in non-flat spacetime
• xPPN: An implementation of the parametrized post-Newtonian formalism using xAct for Mathematica
• Bianchi I cosmological solutions in teleparallel gravity
• Regular solutions in $f(T)$-Yang-Mills theory
• Cosmological singularities in $f(T,\varphi )$ gravity
• Gravitational Waves in New General Relativity
• Teleparallel bigravity
• Spatially Homogeneous Teleparallel Gravity: Bianchi I
• Inhomogeneous solutions in $f(T,B)$ gravity
• Modified Teleparallel $f(T)$ Gravity, DESI BAO and the $H_0$ Tension
• Thermodynamics of the Weyl Geometric Gravity Black Holes
• Teleparallel Geometry with a Single Affine Symmetry
• Spin connection and cosmological perturbations in $f(T)$ gravity
• Magnetic black holes in Weitzenböck geometry
• Conformal Transformations and Cosmological Perturbations in New General Relativity
• First-order formulation of teleparallel gravity and dual loop gravity
• Noether's second theorem in teleparallel gravity
• Teleparallel Minkowski Spacetime with Perturbative Approach for Teleparallel Gravity on a Proper Frame
• The equivalence principle for a plane gravitational wave in torsion based and non-metricity based teleparallel equivalents of general relativity
• The meaning of torsion in teleparallel theories
• Tangent space symmetries in general relativity and teleparallelism
• Spin connection and cosmological perturbations in scalar-torsion gravity
• First-order hyperbolic formulation of the pure tetrad teleparallel gravity theory
• Cosmology in symmetric teleparallel gravity and its dynamical system
• Phase space structure of symmetric teleparallel theory of gravity
• Mass and angular momentum for the Kerr black hole in TEGR and STEGR
• Geometry of teleparallel theories
• The first non-static inhomogeneous exact solution in $f(T,B)$ gravity
• Observational Constraints on Chaplygin Gas Models in Non-Minimally Coupled Power Law $f(Q)$ Gravity with Quasars
• Gauge invariant perturbations of $F(T,T_G)$ Cosmology
• Self-Excited Gravitational Instantons
• Electromagnetic Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity
• Local symmetries in $f(T)$-like models: lessons from 2D
• Kerr-Schild metrics in teleparallel gravity
• Global portraits of nonminimal teleparallel inflation
• Growth factor in teleparallel Gauss-Bonnet gravity
• Off-Shell ADT Conserved Quantities in Palatini Gravity
• Production of Primordial Gravitational Waves in Teleparallel Gravity
• Lost in translation: the Abelian affine connection (in the coincident gauge)
• Die einheitliche Beschreibung der fundamentalen Objekte und Wechselwirkungen der Natur in der Quantentheorie der Ur-Alternativen