Speaker
Description
Extensions of equivalent representations of gravity are discussed in the metric-affine framework. First, we focus on: (i) General Relativity, based upon the metric tensor whose dynamics is given by the Ricci curvature scalar R; (ii) the Teleparallel Equivalent of General Relativity, based on tetrads and spin connection whose dynamics is given by the torsion scalar T; (iii) the Symmetric Teleparallel Equivalent of General Relativity, formulated with respect to both the metric tensor and the affine connection and characterized by the non-metric scalar Q with the role of gravitational field. They represent the so-called Geometric Trinity of Gravity, because, even if based on different frameworks and different dynamical variables, such as curvature, torsion, and non-metricity, they express the same gravitational dynamics. Starting from this framework, we construct their extensions with the aim to study possible equivalence. We discuss the straightforward extension of General Relativity, the f(R) gravity. With this paradigm in mind, the dynamical equivalence is achieved if boundary terms are considered, that is f(T-B) and f(Q-B) theories. Finally, we study the projective transformations in Metric-Affine Theories, considering the general non-metric quadratic gravity, i.e. curvature and nonmetricity. We discuss the conditions under which a projective transformation conserves the Lagrangian. Then we proceed to compute the pertinent geometric variables of a subclass of the most general projective transformations.
