The Physical Metric in General Relativity, Size and Gravitational Lensing of Black Holes and Neutron Stars

Abstract

The physical metric in general relativity has been introduced by the author as the exact solution of Einstein equation that fits the observation of time delay of the solar system. The necessary and sufficient condition for the physical metric is that the speed of light on the angular direction is unchanged from that of vacuum. A striking result is that the radius size of a black hole and a neutron star (summarized as compact object hereafter) is found to be 2.60 times greater than predicted by the Schwarzschild metric. In this article, the gravitational lensing of the compact object at long distance is absent. In other words, it is a feature result of the physical metric that the effect of the gravitational lensing for compact object by itself disappears at long distance. It will be shown that the recent observations are consistent with the prediction of the physical metric.