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.

arXiv comment20 pages, final version. Invited short review published in IJGMMP

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• Neutral regular black hole solution in generalized Rastall gravity
• Scalar QNMs for higher dimensional black holes surrounded by quintessence in Rastall gravity
• Higher dimensional power-Maxwell charged black holes in Einstein and Rastall gravity
• Role of Non-conserved Gravity Theory and Electric Charge in Constructing Complexity-free Stellar Models: A Novel Approach under Non-minimal Coupling
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• Implications of Rastall Theory on Stellar Solutions admitting Vanishing Complexity: A New Perspective
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