The commutator algebra of covariant derivative as general framework for extended gravity. The Rastall theory case and the role of the torsion

Abstract

In this short review, we discuss the approach of the commutator algebra of covariant derivative to analyse the gravitational theories, starting from the standard Einstein's general theory of relativity and focusing on the Rastall theory. After that, we discuss the important role of the torsion in this mathematical framework. In the Appendix of the paper we analyse the importance of the nascent gravitational wave astronomy as a tool to discriminate among the general theory of relativity and alternative theories of gravity.

20 pages, final version. Invited short review published in IJGMMP

References in corpus (13)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Confrontation between General Relativity and Experiment
• Extra force in $f(R)$ modified theories of gravity
• Generalized curvature-matter couplings in modified gravity
• The Brans-Dicke-Rastall theory
• Emergent cosmic space in Rastall theory
• The production of matter from curvature in a particular linearized high order theory of gravity and the longitudinal response function of interferometers
• Gravitational wave astronomy: the definitive test for the "Einstein frame versus Jordan frame" controversy
• Modified GR and Helium Nucleosynthesis
• On Gödel-type Solution in Rastall's Gravity
• Torsion gravity with non-minimally coupled fermionic field: some cosmological models
• Gravity with torsion in non-conservative Maxwell-like gauge approach
• Recovering the fundamental plane of galaxies by $f(R)$ gravity

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• Einstein and Rastall Theories of Gravitation in Comparison
• Accelerated cosmos in a non-extensive setup
• Complexity and Isotropization based Extended Models in the context of Electromagnetic Field: An Implication of Minimal Gravitational Decoupling
• A connection between Rastall-type and f(R, T) gravities
• Role of Non-conserved Gravity Theory and Electric Charge in Constructing Complexity-free Stellar Models: A Novel Approach under Non-minimal Coupling
• Black hole solutions and Euler equation in Rastall and generalized Rastall theories of gravity
• Implications of Rastall Theory on Stellar Solutions admitting Vanishing Complexity: A New Perspective
• Gravitational Analysis of Einstein-Non-Linear-Maxwell-Yukawa Black Hole under the Effect of Newman-Janis Algorithm