Using the mathematical aspects of the Schwarzschild metric, we present different variables transformation which proves that the central singularity hypothesis does not exist. The geometric interpretation of the black hole from the Schwarzschild metric is not mathematically convincing. The different mathematical approaches taken by many authors were viewed, such as the Painleve metric and its complex variant, and the Schwarzschild metric, to deduce a metric with a throat sphere which leads to a mirror space-time. Subsequently, the possibility of a bi-metric tangent to the Schwarzschild metric's throat sphere was deduced. It was also shown that a false interpretation of the variables of the Schwarzschild metric can lead to false physical deductions and, in particular, to the concept of singularity. We computed the general solution of Einstein's equations in the presence of a non-zero energy tensor, that is, for a homogeneous fluid ball with energy conditions. This study method of resolution involves a reformulation of the Einstein equation and integration of the differential system. The metrics found are asymptotic to the Schwarzschild metric outside the fluid ball. Assumptions were presented for the pressure inside the fluid ball and the corresponding metrics were derived. Then, by solving the continuity equation of the energy-impulse tensor, we deduce an expression for the pressure inside the star that permits the express on of the interior and exterior metrics.
Key words: Schwarzs child’s metric, black hole, singularity, gravity, bi-metric, internal metric.
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