Physical metric and the nature of gravity
  A physical metric is defined as one which gives a measurable speed of light throughout the whole space time continuum. It will be shown that a metric which satisfies the condition that speed of light on the spherical direction is that in a vacuum gives a correct result. All the metric functions thus obtained are positive definite and exhibits a repulsive force at short distances. The horizon in the sense of vanishing of the speed of light still exists in the radial direction. It is located at 2.60 times of the Schwarzschild radius. This radius corresponds to the size of a black hole, as well as the photon sphere radius. The metric can be used to calculate general relativistic predictions in higher order for any process. 
Yukio Tomozawa
physics.gen-ph