Local cosmology of the solar system

Abstract

A time-dependent model of space-time is used to describe the gravitational field of the sun. This model is a spherically symmetric approximate solution of Einstein's equations in vacuum. Near the sun it approximates one of the models derived from the Schwarzschild solution, while at large distances it becomes a milne's-like zero space-time curvature model. Two local cosmology free parameters provide simple descriptions for the secular increasing of the astronomical unit, as well as the "anomalous" radial acceleration of the Pioneer probe. We make also a comment about the possibility of deriving MOND's phenomenology from General relativity.