Local cosmology of the solar system

TL;DR

This paper presents a time-dependent, spherically symmetric model of the solar system's gravitational field based on Einstein's equations, explaining phenomena like the increasing astronomical unit and Pioneer anomaly.

Contribution

It introduces a novel local cosmology model with free parameters that describe solar system dynamics and discusses potential links to MOND within general relativity.

Findings

Model approximates Schwarzschild near the sun

Explains secular increase of astronomical unit

Accounts for Pioneer anomaly

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.