Lorentzian geometrical structures with global time, Gravity and Electrodynamics

We investigate Lorentzian structures in the four-dimensional space-time, supplemented either by a covector fifield of the time-direction or by a scalar fifield of the global time. Furthermore, we propose a new metrizable model of the gravity. In contrast to the usual Theory of General Relativity where all ten components of the symmetric pseudo-metrics are independent variables, the presented here model of the gravity essentially depend only on single four-covector fifield, restricted to have only three-independent components. However, we prove that the Gravitational fifield, ruled by the proposed model and generated by some massive body, resting and spherically symmetric in some coordinate system, is given by a pseudo-metrics3, which coincides with the well known Schwarzschild metric from the General Relativity. The Maxwell equations and Electrodynamics are also investigated in the frames of the proposed model. In particular, we derive the covariant formulation of Electrodynamics of moving dielectrics and para/diamagnetic mediums.This is a preprint of the following work: Arkady Poliakovsky, Lorentzian Geometrical Structures with Global Time, Gravity and Electrodynamics, 2023, Springer Cham, reproduced with permission of Springer Nature Switzerland AG 2023. The final authenticated version is available online at: https://doi.org/10.1007/978-3-031-23762-