A Formulation of the Gravitational Equation of Motion
T. Chang
Keywords: principle of equivalence, inertial forces, gravitational field
According to Einstein's principle of equivalence, inertial forces in an accelerated reference system are equivalent to the existence of a gravitational field. In order to formulate the gravitational force as well as inertial forces in explicit form, we introduce two conditions into the 4-D line element and transformations. As a consequence, the equation of motion for gravitational force or inertial force has a form similar to the equation of Lorentz force on a charge in electrodynamics. The inertial forces in non-inertial systems are calculated for two special cases: a uniformly accelerated system, and a uniformly rotating system.
