38 research outputs found
Fermi-normal coordinates for the Newtonian approximation of gravity
In this work, we compute the metric corresponding to a static and spherically
symmetric mass distribution in the general relativistic weak field
approximation to quadratic order in Fermi-normal coordinates surrounding a
radial geodesic. To construct a geodesic and a convenient tetrad transported
along it, we first introduce a general metric, use the Cartan formalism of
differential forms, and then specialize the space-time by considering the
nearly Newtonian metric. This procedure simplifies the calculations
significantly, and the expression for the radial geodesic admits a simple form.
We conclude that in quadratic order, the effects of a Schwarzschild
gravitational field measured locally by a freely falling observer equals the
measured by an observer in similar conditions in the presence of a Newtonian
approximation of gravitation.Comment: Replaced with the version matching the published one in Physica
Script
Effective perihelion advance and potentials in a conformastatic background with magnetic field
An Exact solution of the Einstein-Maxwell field equations for a
conformastatic metric with magnetized sources is study. In this context,
effective potential are studied in order to understand the dynamics of the
magnetic field in galaxies. We derive the equations of motion for neutral and
charged particles in a spacetime background characterized by this class of
solutions. In this particular case, we investigate the main physical properties
of equatorial circular orbits and related effective potentials. In addition, we
obtain an effective analytic expression for the perihelion advance of test
particles. Our theoretical predictions are compared with the observational data
calibrated with the ephemerides of the planets of the Solar system and the Moon
(EPM2011). We show that, in general, the magnetic punctual mass predicts values
that are in better agreement with observations than the values predicted in
Einstein gravity alone.Comment: 11 pages, 6 figures. arXiv admin note: substantial text overlap with
arXiv:1601.0074