12 research outputs found
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 , 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 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 with generalized/ modified scalar
curvature , trace of matter field tensors and modified
Finsler like generating function . 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
-modified gravity using nonholonomic 2+2 splitting
and nonholonomic Finsler like variables . 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 deformations of kerr black holes in Einstein and modified massive gravity and higher dimensions
On relativistic generalization of Perelman’s W-entropy and thermodynamic description of gravitational fields and cosmology
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