Teleparallel gravity

Abstract

In general relativity, the only dynamical field describing the gravitational interaction of matter, is the metric. It induces the causal structure of spacetime, governs the motion of physical bodies through its Levi-Civita connection, and mediates gravity via the curvature of this connection. While numerous modified theories of gravity retain these principles, it is also possible to introduce another affine connection as a fundamental field, and consider its properties - curvature, torsion, nonmetricity - as the mediators of gravity. In the most general case, this gives rise to the class of metric-affine gravity theories, while restricting to metric-compatible connections, for which nonmetricity vanishes, comprises the class of Poincaré gauge theories. Alternatively, one may also consider connections with vanishing curvature. This assumption yields the class of teleparallel gravity theories. This chapter gives a simplified introduction to teleparallel gravity, with a focus on performing practical calculations, as well as an overview of the most commonly studied classes of teleparallel gravity theories.

46 pages, no figures; invited contribution to the book "Signatures and experimental searches for modified and quantum gravity"

References in corpus (7)

• Dark torsion as the cosmic speed-up
• Einstein's Other Gravity and the Acceleration of the Universe
• The teleparallel equivalent of general relativity
• Conformal transformation in $f(T)$ theories
• Post-Newtonian limit of generalized symmetric teleparallel gravity
• Metric-Affine Gravity as an Effective Field Theory
• Variational Principles in Teleparallel Gravity Theories

Cited by in corpus (11)

• Homogeneous and isotropic cosmology in general teleparallel gravity
• A Review of Stable, Traversable Wormholes in f (R) Gravity Theories
• Cosmological solutions in teleparallel $F(T,B)$ gravity
• Scalar Field Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity
• Background-dependent and classical correspondences between $f(Q)$ and $f(T)$ gravity
• Chiral Gravitational Wave Background from Audible Axion via Nieh-Yan Term
• Field transformations and invariant quantities in scalar-teleparallel theories of gravity
• On the global Gaussian bending measure and its applications in stationary spacetimes
• Black hole physics within $f(R)$ gravity: Quasi-normal spectra and greybody factors
• Spatially homogeneous teleparallel spacetimes with four-dimensional groups of motions
• Post-Newtonian limit of generalized scalar-teleparallel theories of gravity