This book investigates Lorentzian structures in the four-dimensional space-time, supplemented either by a covector field of the time-direction or by a scalar field of the global time. Furthermore, it proposes a new metrizable model of gravity. In contrast to the usual General Relativity theory, where all ten components of the symmetric pseudo-metric are independent variables, the gravity model presented here essentially depends only on a single four-covector field, and is restricted to have only three-independent components. However, the author proves that the gravitational field, governed by the proposed model and generated by some massive body, resting and spherically symmetric in some coordinate system, is given by a pseudo-metric that coincides with the well known Schwarzschild metric from General Relativity. The Maxwell equations and electrodynamics are also investigated in the framework of the proposed model. In particular, the covariant formulation of electrodynamics of moving dielectrics and para/diamagnetic media is derived.
Author(s): Arkady Poliakovsky
Publisher: Springer
Year: 2023
Language: English
Pages: 191
City: Cham
Prologue
Contents
1 Preliminary Introduction
References
2 Basic Definitions and Statements of the Main Results
2.1 Generalized-Lorentz's Structures with Time Direction and Global Time
2.1.1 Pseudo-Lorentzian Coordinate Systems
2.2 Kinematical Lorentz's Structure with Global Time
2.3 Kinematical and Dynamical Generalized-Lorentz Structures with Time Direction
2.4 Lagrangian of the Motion of a Classical Point Particle in a Given Pseudo-metric with Time Direction
2.5 Lagrangian of the Electromagnetic Field in a Given Pseudo-metric
2.6 Correlated Pseudo-metrics
2.7 Kinematically Correlated Models of the Genuine Gravity
2.8 Lagrangian for Dynamical Time Direction and Its Limiting Case
2.9 Lagrangian of the Genuine Gravity
References
3 Mass, Charge and Lagrangian Densities and Currents of the System of Classical Point Particles
4 The Total Simplified Lagrangian of the Gravity in a Cartesian Coordinate System
4.1 The Total Simplified Lagrangian in (2.9.23), (2.9.24), for the Limiting Case of (2.9.20) in a Cartesian Coordinate System
5 The Euler-Lagrange for the Lagrangian of the Motion of A Classical Point Particle in a Cartesian Coordinate System
6 The Euler-Lagrange for the Lagrangian of the Gravitational and Electromagnetic Fields in a Cartesian Coordinate System
6.1 The Euler-Lagrange for the Lagrangian in (4.1.71) in a Cartesian Coordinate System
7 Gravity Field of Spherically Symmetric Massive Resting Body in a Coordinate System Which Is Cartesian and Inertial Simultaneously
7.1 Certain Curvilinear Coordinate System in the Case of Stationary Radially Symmetric Gravitational Field and Relation to the Schwarzschild Metric
References
8 Newtonian Gravity as an Approximation of Our Model
8.1 Newtonian Gravity as an Approximation of (6.1.52)
9 Polarization and Magnetization
9.1 Polarization and Magnetization in a Cartesian Coordinate System
10 Detailed Proves of the Stated Theorems, Propositions and Lemmas
Appendix Some Technical Statements
