15,711 research outputs found
Cosmological Attractors and Anisotropies in Two Measure Theories, Effective EYMH systems, and Off--Diagonal Inflation Models
Applying the anholonomic frame deformation method, we construct various
classes of cosmological solutions for effective Einstein -- Yang-Mills --
Higgs, and two measure theories. The types of models considered are
Freedman-Lema\^{i}tre-Robertson-Walker, Bianchi, Kasner and models with
attractor configurations. The various regimes pertaining to plateau--type
inflation, quadratic inflation, Starobinsky type and Higgs type inflation are
presented.Comment: latex2e 11pt, 32 pages; v2 with minor modifications of reference list
and introduction, accepted to EPJ
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
Exact Solutions in Modified Massive Gravity and Off-Diagonal Wormhole Deformations
There are explored off-diagonal deformations of "prime" metrics in Einstein
gravity (for instance, for wormhole configurations) into "target" exact
solutions in f(R,T)-modified and massive/ bi-metric gravity theories. The new
classes of solutions may posses, or not, Killing symmetries and can be
characterized by effective induced masses, anisotropic polarized interactions
and cosmological constants. For nonholonomic deformations with (conformal)
ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small
eccentricity rotoid configurations, we can generate wormholes like objects
matching external black ellipsoid - de Sitter geometries. We conclude that
there are nonholonomic transforms and/or non-trivial limits to exact solutions
in general relativity when modified/ massive gravity effects are modeled by
off-diagonal and/or nonholonomic parametric interactions.Comment: 30 pages, accepted to EJPC; moderators permitted on March 3, 2014, to
resubmit this work from April 1, 201
Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows
We develop an approach to the theory of relativistic geometric flows and
emergent gravity defined by entropy functionals and related statistical
thermodynamics models. Nonholonomic deformations of G. Perelman's functionals
and related entropic values are used for deriving relativistic geometric
evolution flow equations. For self-similar configurations, such equations
describe generalized Ricci solitons defining modified Einstein equations. We
analyze possible connections between relativistic models of nonholonomic Ricci
flows and emergent modified gravity theories. We prove that corresponding
systems of nonlinear partial differential equations, PDEs, for entropic flows
and modified gravity possess certain general decoupling and integration
properties. There are constructed new classes of exact and parametric solutions
for nonstationary configurations and locally anisotropic cosmological metrics
in modified gravity theories and general relativity. Such solutions describe
scenarios of nonlinear geometric evolution and gravitational and matter field
dynamics with pattern-forming and quasiperiodic structure and various space
quasicrystal and deformed spacetime crystal models. We analyze new classes of
generic off-diagonal solutions for entropic gravity theories and show how such
solutions can be used for explaining structure formation in modern cosmology.
Finally, we speculate why the approaches with Perelman-Lyapunov type
functionals are more general or complementary to the constructions elaborated
using the concept of Bekenstein-Hawking entropy.Comment: accepted to EPJC; latex2e 11pt, 35 pages with a table of contents; v3
is substantially modified with a new title and a new co-autho
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
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