Gauge Theories of Gravitation

Abstract

During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge theory of the Weyl-Cartan-Yang-Mills type. The present text offers commentaries on the articles from the most prominent proponents of the theory. In the early 1960s, the gauge idea was successfully applied to the Poincaré group of spacetime symmetries and to the related conserved energy-momentum and angular momentum currents. The resulting theory, the Poincaré gauge theory, encompasses Einstein's general relativity as well as the teleparallel theory of gravity as subcases. The spacetime structure is enriched by Cartan's torsion, and the new theory can accommodate fermionic matter and its spin in a perfectly natural way. This guided tour starts from special relativity and leads, in its first part, to general relativity and its gauge type extensions à la Weyl and Cartan. Subsequent stopping points are the theories of Yang-Mills and Utiyama and, as a particular vantage point, the theory of Sciama and Kibble. Later, the Poincaré gauge theory and its generalizations are explored and special topics, such as its Hamiltonian formulation and exact solutions, are studied. This guide to the literature on classical gauge theories of gravity is intended to be a stimulating introduction to the subject.

arXiv commentLatex, 165 pages, 10 figures, a guide to gauge theories of gravity; v3: pdf submission, v4: Latex, v5: minor corrections

Cited by in corpus (24)

• On the covariance of teleparallel gravity theories
• Observational Tests of Nonlocal Gravity: Galaxy Rotation Curves and Clusters of Galaxies
• Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?
• Constraints on Nonmetricity from Bounds on Lorentz Violation
• New approach to nonrelativistic diffeomorphism invariance and its applications
• On the (non-)uniqueness of the Levi-Civita solution in the Einstein-Hilbert-Palatini formalism
• Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection?
• Constraining Spacetime Nonmetricity with Neutron Spin Rotation in Liquid He-4
• Spin Precession in Inertial and Gravitational Fields
• Tetrads in SU(N) Yang-Mills geometrodynamics
• Weitzenböck's Torsion, Fermi Coordinates and Adapted Frames
• Nonlocal Gravitomagnetism
• The Teleparallel Equivalent of General Relativity and the Gravitational Centre of Mass
• Cartan geometry of spacetimes with a nonconstant cosmological function $\Lambda$
• Galilean gauge theory from Poincare gauge theory
• Projective symmetries and induced electromagnetism in metric-affine gravity
• Non-linearly ghost-free higher curvature gravity
• Torsion or not torsion, that is the question
• A New Action for Nonrelativistic Particle in Curved Background
• A covariant Hamiltonian tetrad approach to numerical relativity
• Sakharov's induced gravity and the Poincaré gauge theory
• Mimetic Tensor-Vector-Scalar Cosmology: Incorporating Dark Matter, Dark Energy and Stiff Matter
• The role of the 1.5 order formalism and the gauging of spacetime groups in the development of gravity and supergravity theories
• Gravitational Energy and the Gauge Theory Perspective