Modified Dynamical Supergravity Breaking and Off-Diagonal Super-Higgs Effects

We argue that generic off-diagonal vacuum and nonvacuum solutions for Einstein manifolds mimic physical effects in modified gravity theories (MGTs) and encode certain models of the $f(R,T,...)$, Ho\v{r}ava type with dynamical Lorentz symmetry breaking, induced effective mass for the graviton etc. Our main goal is to investigate the dynamical breaking of local supersymmetry determined by off-diagonal solutions in MGTs and encoded as effective Einstein spaces. This includes the Deser-Zumino super-Higgs effect, for instance, for a one-loop potential in a (simple but representative) model of $\mathcal{N}=1, D=4$ supergravity. We develop and apply new geometrical techniques which allows us to decouple the gravitational field equations and integrate them in a very general form with the metric and vielbein fields depending on all the spacetime coordinates via means of various generating and integration functions and parameters. We study how solutions in MGTs may be related to the dynamical generation of a gravitino mass and supersymmetry breaking.Comment: latex2e, 33 pages, with table of content; v3 accepted to Class. Quant. Gravit

Off-Diagonal Deformations of Kerr Black Holes in Einstein and Modified Massive Gravity and Higher Dimensions

We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and modified gravity theories when the field equations decouple with respect to certain types of nonholonomic frames of reference. This allows us to construct various classes of exact solutions when the coefficients of the fundamental geometric/ physical objects depend on all spacetime coordinates via corresponding classes of generating and integration functions and/or constants. Such (modified) spacetimes display Killing and non-Killing symmetries, describe nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants. Our method can be extended to higher dimensions which simplifies some proofs for embedded and nonholonomically constrained four-dimensional configurations. We reproduce the Kerr solution and show how to deform it nonholonomically into new classes of generic off-diagonal solutions depending on 3-8 spacetime coordinates. Certain examples of exact solutions are analyzed and that are determined by contributions of new type of interactions with sources in massive gravity and/or modified f(R,T) gravity. We conclude that by considering generic off-diagonal nonlinear parametric interactions in GR it is possible to mimic various effects in massive and/or modified gravity, or to distinguish certain classes of "generic" modified gravity solutions which cannot be encoded in GR.Comment: latex 2e, 11pt, 35 pages with table of content; version 2 modified following Editor's requests and accepted to EPJ

On Relativistic Generalization of Perelman's W-entropy and Statistical Thermodynamic Description of Gravitational Fields

Using double 2+2 and 3+1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in the general relativity, GR, theory. Such F- and W-functionals were introduced in the Ricci flow theory of three dimensional, 3-d, Riemannian metrics by G. Perelman, arXiv: math.DG/0211159. Nonrelativistic 3-d Ricci flows are characterized by associated statistical thermodynamical values determined by W--entropy. Generalizations for geometric flows of 4-d pseudo-Riemannian metrics are considered for models with local thermodynamical equilibrium and separation of dissipative and non-dissipative processes in relativistic hydrodynamics. The approach is elaborated in the framework of classical filed theories (relativistic continuum and hydrodynamic models) without an underlying kinetic description which will be elaborated in other works. The 3+1 splitting allows us to provide a general relativistic definition of gravitational entropy in the Lyapunov-Perelman sense. It increases monotonically as structure forms in the Universe. We can formulate a thermodynamic description of exact solutions in GR depending, in general, on all spacetime coordinates. A corresponding 2+2 splitting with nonholonomic deformation of linear connection and frame structures is necessary for generating in very general form various classes of exact solutions of the Einstein and general relativistic geometric flow equations. Finally, we speculate on physical macrostates and microstate interpretations of the W-entropy in GR, geometric flow theories and possible connections to string theory (a second unsolved problem also contained in Perelman's works) in the Polyakov's approach.Comment: latex2e, v4 is an accepted to EPJC substantial extension of a former letter type paper on 10 pages to a research article on 41 pages; a new author added, the paper's title and permanent and visiting affiliations were correspondingly modified; and new results, conclusions and references are provide

Modified Einstein and Finsler Like Theories on Tangent Lorentz Bundles

We study modifications of general relativity, GR, with nonlinear dispersion relations which can be geometrized on tangent Lorentz bundles. Such modified gravity theories, MGTs, can be modeled by gravitational Lagrange density functionals $f(\mathbf{R},\mathbf{T},F)$ with generalized/ modified scalar curvature $\mathbf{R}$, trace of matter field tensors $\mathbf{T}$ and modified Finsler like generating function $F$. In particular, there are defined extensions of GR with extra dimensional "velocity/ momentum" coordinates. For four dimensional models, we prove that it is possible to decouple and integrate in very general forms the gravitational fields for $f(\mathbf{R},\mathbf{T},F)$-modified gravity using nonholonomic 2+2 splitting and nonholonomic Finsler like variables $F$. We study the modified motion and Newtonian limits of massive test particles on nonlinear geodesics approximated with effective extra forces orthogonal to the four--velocity. We compute the constraints on the magnitude of extra-accelerations and analyze perihelion effects and possible cosmological implications of such theories. We also derive the extended Raychaudhuri equation in the framework of a tangent Lorentz bundle. Finally, we speculate on effective modelling of modified theories by generic off-diagonal configurations in Einstein and/or MGTs and Finsler gravity. We provide some examples for modified stationary (black) ellipsoid configurations and locally anisotropic solitonic backgrounds.Comment: latex2e, 20 pages; version accepted to IJMPD; changed title and modifications following requests of refere

Off-diagonal wormhole and black hole deformations and dark energy in two measure/bi-metric modified gravity theories

We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and two measure/bi-metric modified gravity theories, MGTs, when the field equations decouple with respect to nonholonomic frames of reference. This allows us to construct various classes of exact solutions when the coefficients of the fundamental geometric/physical objects depend on all spacetime coordinates via corresponding classes of generating and integration functions and/or constants. Such (modified) spacetimes display Killing and non-Killing symmetries, describe nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants. Certain examples of exact locally anisotropic wormhole and generic off-diagonal cosmological solutions are analysed for MGTs of massive and/or modified f(R,T) gravity, two measure theory etc. We conclude that considering generic off-diagonal nonlinear parametric interactions in GR it is possible to mimic various effects in massive and/or modified gravity, or to distinguish certain classes of generic modified gravity solutions which cannot be encoded in GR

Nonholonomic ricci flows and Finsler-Lagrange f(R,F,L)-modified gravity and dark matter effects

We review the theory of geometric flows on nonholonomic manifolds and tangent bundles and self-similar configurations resulting in generalized Ricci solitons and Einstein-Finsler equations. There are provided new classes of exact solutions on Finsler-Lagrange f(R,F,L)-modifications of general relativity and discussed possible implications in acceleration cosmology