Lorentzian Geometrical Structures with Global Time, Gravity and Electrodynamics

This book investigates Lorentzian structures in the four-dimensionalspace-time, supplemented either by a covector field of thetime-direction or by a scalar field of the global time. Furthermore,it proposes a new metrizable model of gravity. In contrast to theusual General Relativity theory, where all ten components of thesymmetric pseudo-metric are independent variables, the gravity model presented here essentially depends only on a singlefour-covector field, and is restricted to have onlythree-independent components. However, the author proves that thegravitational field, governed by the proposed model and generated bysome massive body, resting and spherically symmetric in somecoordinate system, is given by a pseudo-metric that coincides with the well knownSchwarzschild metric from General Relativity. The Maxwell equationsand electrodynamics are also investigated in the framework of theproposed model. Inparticular, the covariant formulationof electrodynamics of moving dielectrics and para/diamagneticmedia is derived.