Metric-Affine Gauge Theory of Gravity I. Fundamental Structure and Field Equations

Abstract

We give a self-contained introduction into the metric-affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang-Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric-affine gravity. The results are put into the dynamical framework of a classical field theory. We derive subcases of metric-affine gravity by restricting the affine group to some of its subgroups. The important subcase of general relativity as a gauge theory of translations is explained in detail.

43 pages, LaTeX, six .eps figures included, uses lscape.sty, to appear in Int. J. Mod. Phys. D

Cited by in corpus (55)

• Field equations in teleparallel spacetime: Einstein's Fernparallelismus approach towards unified field theory
• Quasilocal quantities for GR and other gravity theories
• Searches for the role of spin and polarization in gravity
• Constraining Torsion with Gravity Probe B
• Regularizing role of teleparallelism
• Metric-affine gauge theory of gravity II. Exact solutions
• A Higgs Mechanism for Gravity
• Covariance properties and regularization of conserved currents in tetrad gravity
• Local symmetries and physical degrees of freedom in $f(T)$ gravity: a Dirac Hamiltonian constraint analysis
• A special exact spherically symmetric solution in f(T) gravity theories
• Gravitational Goldstone fields from affine gauge theory
• Can Gravity Probe B usefully constrain torsion gravity theories?
• Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?
• Energy and momentum of a spherically symmetric dilaton frame as regularized by teleparallel gravity
• Torsion waves in metric-affine field theory
• Modified gravity realizations of quintom dark energy after DESI DR2
• Volume elements of spacetime and a quartet of scalar fields
• The quadratic spinor Lagrangian is equivalent to the teleparallel theory
• Teleparallel Gravity and Dimensional Reductions of Noncommutative Gauge Theory
• A small guide to variations in teleparallel gauge theories of gravity and the Kaniel-Itin model
• Conserved currents in gravitational models with quasi-invariant Lagrangians: Application to teleparallel gravity
• Radiatively stable ghost and tachyon freedom in Metric Affine Gravity
• The Perfect Hyperfluid of Metric-Affine Gravity: The Foundation
• Primordial black holes and induced gravitational waves from double-pole inflation
• Invariant conserved currents in gravity theories: diffeomorphisms and local gauge symmetries
• The energy-momentum of plane-fronted gravitational waves in the teleparallel equivalent of GR
• Translations and dynamics
• $D=4$ topological gravity from gauging the Maxwell-special-affine group
• Coframe teleparallel models of gravity. Exact solutions
• BRST-antifield-treatment of metric-affine gravity
• Energy of spherically symmetric spacetimes on regularizing teleparallelism
• Solutions without singularities in gauge theory of gravitation
• Invariant conserved currents in generalized gravity
• Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity
• Geometrical Foundations of Cartan Gauge Gravity
• Dynamical reconstruction of the $\Lambda$CDM model in the scalar-tensor representation of $f\left(Q,T\right)$ gravity
• Quadratic Metric-Affine Gravity: Solving for the Affine-Connection
• Goedel type solution in teleparallel gravity
• Gravitational waves in metric-affine gravity theory
• Isomorphism between Non-Riemannian gravity and Einstein-Proca-Weyl theories extended to a class of Scalar gravity theories
• Constraining Palatini gravity with GR-independent equations of state for neutron stars
• Bondi-Sachs energy-momentum and the energy of gravitational radiation
• Magnetic black holes in Weitzenböck geometry
• Teleparallel Gravity in Five Dimensional Theories
• Cosmic inflation from broken conformal symmetry
• Motion in gauge theories of gravity
• An assessment of Evans' unified field theory I
• Friedmann cosmology with hyperfluids
• On the extension of the Obukhov theorem in non-Riemannian gravity I
• Gravitational waves and the breaking of parallelograms in space-time
• Thermodynamics in dynamical spacetimes
• About the (in)equivalence between holonomic versus non-holonomic theories of gravity
• On the Regularization of Kerr-NUT spacetime: I
• A gauge theoretical view of the charge concept in Einstein gravity
• On the triviality of certain non-Riemannian models of gravitation