Comparing Equivalent Gravities: common features and differences

Abstract

We discuss equivalent representations of gravity in the framework of metric-affine geometries pointing out basic concepts from where these theories stem out. In particular, we take into account tetrads and spin connection to describe the so called {\it Geometric Trinity of Gravity}. Specifically, we consider General Relativity, constructed upon the metric tensor and based on the curvature $R$; Teleparallel Equivalent of General Relativity, formulated in terms of torsion $T$ and relying on tetrads and spin connection; Symmetric Teleparallel Equivalent of General Relativity, built up on non-metricity $Q$, constructed from metric tensor and affine connection. General Relativity is formulated as a geometric theory of gravity based on metric, whereas teleparallel approaches configure as gauge theories, where gauge choices permit not only to simplify calculations, but also to give deep insight into the basic concepts of gravitational field. In particular, we point out how foundation principles of General Relativity (i.e the Equivalence Principle and the General Covariance) can be seen from the teleparallel point of view. These theories are dynamically equivalent and this feature can be demonstrated under three different standards: (1) the variational method; (2) the field equations; (3) the solutions.

arXiv comment30 pages, 6 figures

References in corpus (58)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Extended Theories of Gravity
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• The Cosmological Constant
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• f(T) teleparallel gravity and cosmology
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• First M87 Event Horizon Telescope Results. II. Array and Instrumentation
• Coincident General Relativity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• First M87 Event Horizon Telescope Results. III. Data Processing and Calibration
• Physics, Astrophysics and Cosmology with Gravitational Waves
• The teleparallel equivalent of general relativity
• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• The Stueckelberg Field
• Testing General Relativity with Pulsar Timing
• Modified teleparallel theories of gravity
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Strong-field Gravity Tests with the Double Pulsar
• A review of the discovery reach of directional Dark Matter detection
• Gravity, Gauge Theories and Geometric Algebra
• Dark matter, dark energy, and alternate models: A review
• Black holes in $f(\mathbb{Q})$ Gravity
• Noether Symmetry Approach in $f(T,B)$ teleparallel cosmology
• No further gravitational wave modes in $F(T)$ gravity
• Modified teleparallel theories of gravity in symmetric spacetimes
• Precision Gravity Tests and the Einstein Equivalence Principle
• Conformal aspects of Palatini approach in Extended Theories of Gravity
• The dynamics of metric-affine gravity
• Conformal Gravity and Transformations in the Symmetric Teleparallel Framework
• Hamiltonian and primary constraints of new general relativity
• Gravitational waves in modified teleparallel theories of gravity
• Addressing the missing matter problem in galaxies through a new fundamental gravitational radius
• The gravitational energy-momentum pseudotensor: the cases of $f(R)$ and $f(T)$ gravity
• Weyl geometry
• Lessons of spin and torsion: Reply to ``Consistent coupling to Dirac fields in teleparallelism"
• On an integrable geometrical foundation of gravity
• Gravitational waves in Poincaré gauge gravity theory
• The $3+1$ Formalism in the Geometric Trinity of Gravity
• Testing General Relativity in the Solar System: present and future perspectives
• Role of spacetime boundaries in Einstein's other gravity
• Deriving the mass of particles from Extended Theories of Gravity in LHC era
• Reaching the sensitivity limit of a Sagnac gyroscope through linear regression analysis
• Solar-system tests of the relativistic gravity
• A review about Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry
• Gravity and the Quantum: Are they Reconcilable?
• Universality of the Einstein theory of gravitation
• Lorentz Connections and Gravitation
• Bringing Together Gravity and the Quanta

Cited by in corpus (89)

• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• The role of the boundary term in $f(Q,B)$ symmetric teleparallel gravity
• Slow-roll inflation in $f(Q)$ non-metric gravity
• Non-metricity with bounday terms: $f(Q,C)$ gravity and cosmology
• A class of static spherically symmetric solutions in $f(Q)$-gravity
• Forecasting constraints on deviations from general relativity in $f(Q)$ gravity with standard sirens
• On the viability of $f(Q)$ gravity models
• Non-Local Gravity Wormholes
• Minisuperspace quantum cosmology in $f(Q)$ gravity
• Data reconstruction of the dynamical connection function in $f(Q)$ cosmology
• Static and spherically symmetric wormholes in metric-affine theories of gravity
• Phase-space analysis of a novel cosmological model in $f(Q)$ theory
• The effective field theory approach to the strong coupling issue in $f(T)$ gravity
• Analytical results for binary dynamics at the first post-Newtonian order in Einstein-Cartan theory with the Weyssenhoff fluid
• Testing $\Lambda$-Free f(Q) Cosmology
• Quasinormal modes, thermodynamics and shadow of black holes in Hu-Sawicki f(R) gravity theory
• Observational test for $f(Q)$ gravity with weak gravitational lensing
• Exploring the stability of $f(Q)$ cosmology near general relativity limit with different connections
• Constraints on $f(Q)$ logarithmic model using gravitational wave standard sirens
• Black hole shadow and chaos bound violation in $f(T)$ teleparallel gravity
• The Non-Relativistic Geometric Trinity of Gravity
• Black holes and regular black holes in coincident $f(\mathbb{Q},{\mathbb{B}}_Q)$ gravity coupled to nonlinear electrodynamics
• Structure growth in $f(Q)$ cosmology
• Underdetermination in Classic and Modern Tests of General Relativity
• Ghost and Laplacian Instabilities in the Teleparallel Horndeski Gravity
• Gravitational tensor and scalar modes in $f(Q,B)$ non-metric gravity
• Stability of $f(Q,B)$ Gravity via Dynamical System Approach: a Comprehensive Bayesian Statistical Analysis
• Unexplored regions in teleparallel $f(T)$ gravity: Sign-changing dark energy density
• FLRW Cosmology in Metric-Affine $F(R,Q)$ Gravity
• Cosmic Growth in $f(T)$ Teleparallel Gravity
• Growth of structures using redshift space distortion in $f(T)$ Cosmology
• Chebyshev cosmography in the framework of extended symmetric teleparallel theory
• Dynamical system analysis of Dirac-Born-Infeld scalar field cosmology in coincident $f(Q)$ gravity
• Preserving quantum information in $f(Q)$ cosmology
• Influence of pressure anisotropy and non-metricity parameter on mass-radius relation and stability of millisecond pulsar in $f(Q)$ gravity
• Gravity from Pre-geometry
• Exploring departures from Schwarzschild black hole in $f(R)$ gravity
• Myrzakulov $F(T,Q)$ gravity: cosmological implications and constraints
• The amplification of cosmological magnetic fields in Extended $f(T,B)$ Teleparallel Gravity
• Gibbons-Hawking-York boundary terms and the generalized geometrical trinity of gravity
• Maxwell-$f(Q)$ theory
• Dynamical system analysis of LRS-BI Universe with f(Q) gravity theory
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• Cosmological Inflation and Meta-Empirical Theory Assessment
• Spatially covariant gravity with nonmetricity
• Reconstructions of $f(\mathcal{P})$ and $f(\mathcal{Q})$ gravity models from $(m,n)$-type Barrow Holographic Dark Energy: Analysis and Observational Constraints
• Fundamental Physics and Cosmology with TianQin
• The effective Equation of State in Palatini $f(R)$ cosmology
• Stable $f(Q)$ gravity model through non-trivial connection
• Late-time dynamics of dark energy EoS in symmetric teleparallel gravity
• Extended Geometric Trinity of Gravity
• Interaction between linear polarized plane gravitational waves and a plane electromagnetic wave in the electromagnetic-gravity analogue
• Extended Bose-Einstein condensate dark matter in $f(Q)$ gravity
• The Equivalence Principle as a Noether Symmetry
• $f(T)$ Gravity: Background Dependence and Propagating Degrees of Freedom
• Comparing measures of the Hubble and BAO tensions in $\Lambda$CDM and possible solutions in $f(Q)$ gravity
• Kinematics in Metric-Affine Geometry
• The equivalence principle for a plane gravitational wave in torsion based and non-metricity based teleparallel equivalents of general relativity
• Local Limit of Nonlocal Gravity: A Teleparallel Extension of General Relativity
• Cosmic Evolution of the Kantowski-Sachs Universe in the Context of a Bulk Viscous String in Teleparallel Gravity
• Spinning (A)dS Black Holes with Slow-Rotation Approximation in Dynamical Chern-Simons Modified Gravity
• Conventionalism, cosmology and teleparallel gravity
• Field transformations and invariant quantities in scalar-teleparallel theories of gravity
• Propagating Gravitational Waves in Teleparallel Gauss-Bonnet Gravity
• Dark matter effects in modified teleparallel gravity
• Is spacetime curved? Assessing the underdetermination of general relativity and teleparallel gravity
• Polytropic Stars in $f(Q)=Q+\xi Q^2$ covariant formulation
• On parity-odd sector in metric-affine theories
• Probing symmetric teleparallel gravity in the early universe
• New gravitational wave polarization modes in the torsionless spacetime
• Mass and angular momentum for the Kerr black hole in TEGR and STEGR
• The general expression for $f(T)$ in a charged cylindrical spacetime with diverse dimensions
• Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry
• Equivalent Gravities and Equivalence Principle: Foundations and experimental implications
• Static, Cylindrically Symmetric Spacetimes in the Coincident f(Q) Gravity
• Post-Newtonian limit of generalized scalar-teleparallel theories of gravity
• Does the metric play a fundamental role in the building of gravitational models?
• Confronting eikonal and post-Kerr methods with numerical evolution of scalar field perturbations in spacetimes beyond Kerr
• Minisuperspace Cosmology in Extended Geometric Trinity of Gravity
• The gravitational energy-momentum pseudo-tensor in $f(Q)$ non-metric gravity
• Issue of Branched Hamiltonian, Inflation and indispensability of scalar field in generalized Teleparallel theories
• White Dwarf Envelops and Temperature Corrections in Exponential $f(T)$ Gravity
• Comparison of Quasinormal Modes of Black Holes in $f(\mathbb{T})$ and $f(\mathbb{Q})$ Gravity
• Generalized Second Law and Thermodynamical Aspects of $f(Q,\mathcal{T})$ Gravity
• Symmetric teleparallel gravitational effects on solar neutrino oscillations
• Growth factor in teleparallel Gauss-Bonnet gravity
• Inflation and primordial fluctuations in $f(Q,T)$ gravity
• The $f(Q)$ gravity and affine EoS: Compatibility and observational constraints
• Insights in $f(Q)$ cosmology: the relevance of the connection