Solution of Einsteins equations, for a fluid and homogeneous star

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