The Solution of the Einstein’s Equations in the Vacuum Region Surrounding a Spherically Symmetric Mass Distribution

Abstract

In this article, we address the solution of the Einstein’s equations in the vacuum region surrounding a spherically symmetric mass distribution. There are two different types of mathematical solutions, depending on the value of a constant of integration. These two types of solutions are analysed from a physical point of view. The comparison with the linear theory limit is also considered. This leads to a new solution, different from the well known one. If one considers the observational data in the weak field limit this new solution is in agreement with the available data. While the traditional Schwarzschild solution is characterized by a horizon at r = 2 G M / c 2 , no horizon exists in this new solution.