Generic off-diagonal solutions and jet deformations in modified and/or higher dimension gravity theories

Let g be a pseudo–Riemanian metric on a manifold V with conventional n+n dimensional splitting, n ≥ 2, for a nonholonomic (non–integrable) distribution N and consider a correspondingly adapted linear metric compatible connection $\widehat{\mathbf{\text{D}}}$ and its torsion $\widehat{T}$, both completely determined by g. We prove that there are certain generalized frame and/or jet transforms and prolongations with $\left(\mathbf{\text{g}},\mathbf{\text{V}}\right)\to \left(\widehat{\mathbf{\text{g}}},\widehat{\mathbf{\text{V}}}\right)$ into explicit classes of solutions of some generalized Einstein equations $\widehat{\mathbf{\text{R}}}\text{i}\text{c}=\text{Λ}\widehat{\mathbf{\text{g}}},\text{Λ}=\mathit{\text{const}}$, encoding various types of (nonholonomic) Ricci soliton configurations and/or jet variables and symmetries, in particular, subject to the condition $\widehat{T}=0$. This allows us to construct in general form generic off–diagonal exact solutions depending on all space time coordinates on V and its jet prolongations, via generating and integration functions and various classes of constants and associated symmetries. We consider an example when exact solutions are constructed as nonholonomic jet prolongations of the Kerr metrics, with possible Ricci soliton deformations, and characterized by generalized connections.