Spacetime geometry is described by two -- {\em a priori} independent -- geometric structures: the symmetric connection $Γ$ and the metric tensor $g$. Metricity condition of $Γ$ (i.e. $\nabla g = 0$) is implied by the Palatini variational principle, but only when the matter fields belong to an exceptional class. In case of a generic matter field, Palatini implies non-metricity of $Γ$. Traditionally, instead of the (1st order) Palatini principle, we use in this case the (2nd order) Hilbert principle, assuming metricity condition {\em a priori}. Unfortunately, the resulting right-hand side of the Einstein equations does not coincide with the matter energy-momentum tensor. We propose to treat seriously the Palatini-implied non-metric connection. The conventional Einstein's theory, rewritten in terms of this object, acquires a much simpler and universal structure. This approach opens a room for the description of the large scale effects in General Relativity (dark matter?, dark energy?), without resorting to purely phenomenological terms in the Lagrangian of gravitational field. All theories discussed in this paper belong to the standard General Relativity Theory, the only non-standard element being their (much simpler) mathematical formulation. As a mathematical bonus, we propose a new formalism in the calculus of variations, because in case of hyperbolic field theories the standard approach leads to nonsense conclusions.
A Cartan-geometrical perspective on torsion and non-metricity
Scuola Superiore Meridionale（南方高等学院）；INFN– Sezione di Napoli（那不勒斯意大利国家核物理研究所）；University of Tartu（塔尔图大学）；Institute of Theoretical Physics and Astrophysics, University of Gdańsk（格但斯克大学理论物理与天体物理研究所）
Wald Entropy in Extended Modified Myrzakulov Gravity Theories: \(f(R, T, Q, R_{μν}T^{μν}, R_{μν}Q^{μν}, \dots)\)
Northeast Community College（东北社区学院）；Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics（拉特拜·米尔扎库洛夫欧亚理论物理中心）；L. N. Gumilyov Eurasian National University（L.N. 古米廖夫欧亚国立大学）
Equivalence Principle violation in metric-affine gravity and finite-temperature effects
Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；Università degli Studi di Napoli “Federico II”（那不勒斯费德里科二世大学）；Scuola Superiore Meridionale（南方高等学院）；Università degli Studi di Salerno（萨莱诺大学）
