Note on Relativistic Mechanics

Source abstract

The object of this note is to derive a form of Poisson's equation from general relativistic mechanics, without assuming the field to be either static or “weak”. The problem is essentially a “local” problem, all observations being made by one observer; this observer determines the apparent gravitational field in his vicinity by observing the motions of free (isolated) particles. Defining gravitational mass by means of Poisson's equation, we find the relation between the densities of gravitational and inertial mass relative to any observer. We also find what may be called the non-rotating frame of reference belonging to any observer.