About Uniqueness of Steady Ricci Schwarzschild Solitons

In this paper, the uniqueness of steady Schwarzschild gradient Ricci solitons is studied. The role of the weight functions is analyzed. The generalized steady Schwarzschild gradient Ricci solitons are investigated; the implications of the rotational ansatz of Bryant are developed; and the new Generalized Schwarzschildsteady gradient solitons are defined. The aspects of the weight functions of the latter type of solitons are researched as well. The new most-accurate curvature bound of the steady Ricci gradient solitons is provided. The uniqueness of the Schwarzschild solitons is discussed. The Ricci flow is reconciled with the Einstein Field Equations such that the weight functions are utilized to spell out the determinant of the metric tensor, the procedure for which is commented on following the use of the appropriate geometrical objects. The mean curvature is discussed. The configurations of the observer are issued from the geodesics spheres of the solitonic structures.