Nonholonomic Ricci Flows: V. Parametric Deformations of Solitonic pp–Waves and Schwarzschild Solutions

We study Ricci flows of some classes of physically valuable solutions in Einstein and string gravity. The anholonomic frame method is applied for generic off–diagonal metric ansatz when the field/ evolution equations are transformed into exactly integrable systems of partial differential equations. The integral varieties of such solutions, in four and five dimensional gravity, depend on arbitrary generation and integration functions of one, two and/ or three variables. Certain classes of nonholonomic frame constraints allow us to select vacuum and/or Einstein metrics, to generalize such solutions for nontrivial string (for instance, with antisymmetric torsion fields) and matter field sources. A very important property of this approach (originating from Finsler and Lagrange geometry but re–defined for semi–Riemannian spaces) is that new classes of exact solutions can be generated by nonholonomic deformations depending on parameters associated to some generalized Geroch transforms and Ricci flow evolution. In this paper, we apply the method to construct in explicit form some classes of exact solutions for multi–parameter Einstein spaces and their nonholonomic Ricci flows describing evolutions/interactions of solitonic pp–waves and deformations of the Schwarzschild metric. We explore possible physical consequences and speculate on their importance in modern gravity.