Coordinate Independence and a Physical Metric in Compact Form

Abstract

A physical metric is constructed as one that gives a coordinate independent result for the time delay in infinite order in the perturbation expansion in the gravitational constant. A compact form for the metric is obtained. One result is that the metric functions are positive definite. Another is an exact expression for the gravitational red shift. The metric can be used to calculate general relativity predictions in higher order for any process. A relationship between the spacetimes of the physical metric and the Schwarzschild metric is discussed.