Relativistic Physics in Arbitrary Reference Frames de Nikolai Mitskievich

Relativistic Physics in Arbitrary Reference Frames

Nikolai Mitskievich

The concept of reference frame was introduced in physics at an early stage when its formalisation had just begun and even before introduction of systems of co-ordinates and equations of motion; this concept continues to play a fundamental role in science ever since. In this book, the author considers mainly the problem of the description and further applications of reference frames in relativistic physics primarily using a general relativistic approach to them.

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Cuprins

Preface; Introduction; A general characterisation of the subject; A synopsis of notations of Riemannian geometry; The Noether theorem: space-time invariance; The Noether densities transformation laws; Reference frames calculus; The monad formalism and its place in the description of reference frames in relativistic physics; Reference frames algebra; Geometry of congruences. Acceleration, rotation, expansion and shear of a reference frame; Differential operations and identities of the monad formalism; Equations of motion of test particles; The electric field strength and magnetic displacement vectors; Monad description of the motion of a test charged mass in gravitational and electromagnetic fields; Motion of photons, the redshift and Doppler effects; The dragging phenomenon; Dragging in circular equatorial orbits in the Kerr space-time; An orbit shift in the TaubNUT space-time; Dragging in the space-time of a pencil of light; Other dragging effects; More general gravitoelectromagnetic and gravitoelectric phenomena; The Maxwell field equations; The four-dimensional Maxwell equations; The electromagnetic stress-energy tensor and its monad decomposition; Monad representation of Maxwells equations; A charged fluid without electric field; An Einstein-Maxwell field with kinematic magnetic charges; The Einstein field equations; The four-dimensional Einstein equations; Monad representation of Einsteins equations; The geodesic deviation equation and a new level of analogy between gravitation and electromagnetism; New quasi-Maxwellian equations of the gravitational field; Remarks on classification of intrinsic gravitational fields; Example of the Taub-NUT field; Example of the spinning pencil-of-light field; Gravitational fields of the G¨odel universe; Perfect fluids; Introductive remarks; Rank 2 and 3 fields; Free rank 2 field; Free rank 3 field; Rotating fluids; Special relativistic theory; Additional remarks; Mechanics versus field theory; Canonical approach to field theory; Canonical formalism and quantisation; Concluding remarks; References; Index.