We'd like to understand how you use our websites in order to improve them. Register your interest. This paper shows that this assumption, although widespread and apparently trivial, leads to an anisotropy of the velocity of two light beams traveling in opposite directions along the rim of the disk, which in turn implies some recently pointed out paradoxical consequences undermining the self-consistency of the special theory of relativity SRT. A correct application of the SRT solves the problem and recovers complete internal consistency for the theory. As an immediate consequence, it is shown that the Sagnac effect only depends on the nonhomogeneity of time of the platform and has nothing to do with any anisotropy of the speed of light along the rim of the disk, contrary to an incorrect but widely held idea. This is a preview of subscription content, log in to check access.
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Theoretical Physics. First Part. Newtonian equilibrium systems: Politropic Equations of state. Equations of Lane-Emden. Numerical and analitic solutions of the Lane Emden equations.
Scaling laws in the solutions: homoteties. Isothermal configurations. Self gravitating systems in uniform rotation. Self gravitating systems with uniform vorticity. Inhomogeneous self gravitating systems with rotation and vorticity. The virial theorem of order n. A functional approach to the configurations of equilibrium. Equilibrium configurations of fermions and bosons: The Thomas-Fermi atom. Thomas-Fermi atoms at finite temperature.
Self gravitating systems of fermions at zero and at finite temperature. The concept of cut-off in the phase space. Self gravitating systems of bosons at zero temperature and at finite temperature.
White dwarfs and neutron stars. Scaling laws. The concept of critical mass. Newton gravitational theory: Tests of inverse square law. The gravitational potential. Gravitational multipoles. The equivalence of inertial and gravitational mass and its experimental verification, on the ground and in space. Tidal forces. Special relativity: The principle of special relativity. Lorentz transformations. The Minkowski space. Relativistic invariant field equations.
The relativistically invariant formulation of the motion of a free particle. The relativistically invariant formulation of the field equations for a free field: the case of the electric field. The electromagnetic interactions: the Maxwell equations and the Proca equations. Doppler shift. The equations of motion of a charged particle. Derivation of the Maxwell equations from a Lagrangian formulation.
Relativistically invariant theory of Gravitation: The linear field equations of gravitation. The interaction of gravitation and matter. The variational principle and the equation of motion. The non relativistic limit and newton theory. The geometric interpretation. Curved space-time. Applications of the linear theory: The field of a spherical mass. The gravitational time dilatation. The deflection of light. The retardation of light.
Gravitational lenses. The field of a rotating mass. The Lense-Thirring effect. Gravitational waves: Plane waves. The emission of gravitational waves. Emission by a vibrating quadrupole. Emission by a rotating quadrupole. Emission of bursts of gravitational radiation. The quadrupole detector and its cross section. Experiments with Detectors of gravitational radiation. References :. Second Part. Riemannian geometry: General coordinates and tensors.
Affine Spaces. Parallel transport: the covariant derivative. The affine geodesic equations. The Riemann tensor. The metric spaces. The metric geodesic equations. Geodesic deviation and tidal fields. Isometries of. Conserved quantities. The principle of general relativity: Einstein field equations. Variational principles. The Palatini approach. Stationary and static space-times. Solutions with spherical symmetry.
The Birkhoff theorem. The Schwarschild solution. The motion of planets: the perihelion. The Hamilton Jacobi Equation. Positive and negative energy states. The propagation of light: the gravitational red shift. Geodetic precession. The energy momentum tensor. The relativistic equations of equilibrium of a star. The Tolmann-Oppenheimer-Volkoff equation of equilibrium. Stabilty of the equilibrium configurations. Eigenfrequencies of pulsation of a star.
The maximum mass of a Neutron Star. Singularities and pseudo singularities: The black hole and the horizon. Kruskall diagrams. The maximal extension of a Schwarschild geometry. The Kerr solution. The Kerr- Newmann solution. Capture of particles from black holes. Effective potential. Circular orbits. The positive and negative energy states. Horizons and singularities in the Kerr and Kerr-Newmann geometries.
Electric and magnetic fields of black holes. Black holes in our galaxy. The paradigm of identification of Black Holes. Collapseng shells.
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Speed of Light on Rotating Platforms
We'd like to understand how you use our websites in order to improve them. Register your interest. It has been suggested by Usov that accreting white dwarfs, collapsing to neutron stars may be the sources of the gamma-ray bursts observed at cosmological distances, provided they rotate very fast and have enormously high magnetic fields. The problem with Usov's proposal is reduced by incorporating the relativistic corrections for fast rotating magnetic dipoles Belinsky et al.