Study of central field in general relativity

In this paper, we have developed the complete equations of gravity central field in general relativity. We do not restrict to vacuum solutions, or static solutions, or solutions without cosmological constant. We work with the field equations for non-zero stress-energy tensor, in its two variables: temporal and radial coordinates and we will include a section for solutions with non-zero cosmological constant. Our objective is to find the expressions of the components of the metric tensor as a function of the components of the stress-energy tensor also to find the relationships to be satisfied between the components of the stress?energy tensor in order to create a central field. This paper has a certain didactic meaning. For this reason, some developments are indicated to help the readers in their calculations.