Overview and perspectives on metric-affine gravity

Abstract

The main purpose of this work is to give an overview of a generalization of the theory of general relativity, namely metric-affine gravity. We rederive an expression for the Lie derivative of the metric in the case of metric-affine theory and discuss some consequences of such an expression. As a gauge theory of gravitation it may be considered as an upshot of a gauging procedure of the general affine group, or its double covering. A historical approach of such a theory is also contained including the key results. One concludes with some perspectives on the calculation of topological observables in that theory viewed as topological gravity theory.

In Pursuit of BRST Symmetry and Observables in 4D Topological Gauge-Affine Gravity

“…One should stress that metric-affine gauge theory of gravity could be well-described after a gauging process of the affine group or its double-covering à la Weyl-Yang-Mills, in terms of a couple of gauge potentials (ϑ a , Γ ab ), with ϑ a denoting the coframe 1-forms and Γ ab being spacetime connection 1-forms [50] (see [35] for an exhaustive and self-contained review). Moreover, a metric must be added by hand for physical reasons related to causality and measurements of lengths and angles.…”

Affine Differential Geometric Control Tools for Statistical Manifolds

“…(IV)-through the dual connection ∇ * in (2), such that T ∇ = T ∇ * = 0. (V)-through the dual connection ∇ * in (2), such that both A, A are symmetric.…”

“…The geometrization based on both a semi-Riemannian metric and an affine connection was already used (until now, without great succes) in different attempts to unify relativistic gravity models with electromagnetism ones (Weyl, Eddington, Einstein, Kaluza, etc., in the first half of the 20th century; see in [2] for a recent review). Instead, in Statistics, the model was considered important and fruitful.…”

In Quest of BRST Symmetry and Observables in 4D Topological Gauge-Affine Gravity

“…Moreover, as a formalism we choose to use the superconnection formalism, cf. [36]. Our paper is organized as follows: In the next section, using the superspace approach BRST-anti-BRST algebra [37] for a topological gauge-affine model of gravity is obtained, which seems to be nilpotent off-shell.…”