On a physical interpretation of the Schwarzschild metric

Abstract

A method is devised for giving a physical interpretation to the customary Schwarzschild coordinates in the vicinity of a charged or uncharged isolated mass. The construction is accomplished by introducing systems that are allowed to freely fall in toward the mass from infinity (drift-systems). It is demonstrated that the Schwarzschild spatial coordinates and their increments have a full physical significance in terms of rod and clock measurements performed in the drift-systems. The time coordinate and its increment are not so amenable to treatment and cannot be considered as having been given such physical significance. In the discussion the Schwarzschild metric about an uncharged and charged mass is derived, in part, by heuristic classical arguments employing conservation of energy. The arguments are then shown to be valid by consulting the Field Equations. In the derivation the gravitational singularity (at 2GM/C2) takes on the significance of being the location at which a drift-system achieves the speed of light relative to a proper system at the same point.