Lorentzian Geometrical Structures with Global Time, Gravity and Electrodynamics
portes grátis
Lorentzian Geometrical Structures with Global Time, Gravity and Electrodynamics
Poliakovsky, Arkady
Springer International Publishing AG
02/2024
189
Mole
Inglês
9783031237645
15 a 20 dias
Descrição não disponível.
1. Preliminary introduction.- 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.- 3. Mass, charge and Lagrangian densities and currents of the system of classical point particles.- 4. The total simplified Lagrangian in (2.9.23), (2.9.24), for the limiting case of (2.9.20) in a cartesiancoordinate 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 (4.0.71) 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.- 8. Newtonian gravity as an approximation of (6.0.52).- 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.- 11. Appendix: sometechnical statements.
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Electrodynamics;Pseudo-Metrics;Lorentzian Geometrical Structures;Global Time;Gravity
1. Preliminary introduction.- 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.- 3. Mass, charge and Lagrangian densities and currents of the system of classical point particles.- 4. The total simplified Lagrangian in (2.9.23), (2.9.24), for the limiting case of (2.9.20) in a cartesiancoordinate 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 (4.0.71) 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.- 8. Newtonian gravity as an approximation of (6.0.52).- 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.- 11. Appendix: sometechnical statements.
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