Geometric flows and Perelman’s thermodynamics for black ellipsoids in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> and Einstein gravity theories

Gheorghiu, Tamara; Ruchin, Vyacheslav; Vacaru, Olivia; Vacaru, Sergiu I.

doi:10.1016/j.aop.2016.02.008

Cited by 20 publications

(15 citation statements)

References 27 publications

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“…Arnowitt-Deser-Misner, formalism in GR can be found, for instance, in [57][58][59]74]. In order to construct new classes of cosmological solutions, we shall apply the anholonomic frame deformation method, AFDM (see details and examples for accelerating cosmology and DE and DM physics in [49,52,[75][76][77]).…”

Section: Introductionmentioning

confidence: 99%

Anamorphic quasiperiodic universes in modified and Einstein gravity with loop quantum gravity corrections

Amaral

Aschheim

Bubuianu

et al. 2017

Class. Quantum Grav.

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Heterotic supergravity with internal almostKähler spaces; instantons for SO(32) AbstractThe goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/aperiodic/fractal/stochastic/ (super) cluster/filament/polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such Made open access 13 September 2017Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. solutions are characterized by nonlinear symmetries of generating functions for generic off-diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi-Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.

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Section: Introductionmentioning

confidence: 99%

Anamorphic quasiperiodic universes in modified and Einstein gravity with loop quantum gravity corrections

Amaral

Aschheim

Bubuianu

et al. 2017

Class. Quantum Grav.

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“…We note that nonassociative geometric flow evolution theories and applications have not been studied in modern mathematics and physics. There were elaborated only approaches related to noncommutative geometry (a lá A. Connes), [ 15 ] geometric and quantum information flow theories and modified gravity; [ 6–8,62 ] and, in associative/commutative form, it is performed a recent research on swampland conjectures and Ricci flows. [ 23,24,26,27 ] Our nonassociative geometric models and solutions are self‐consistent and well‐defined in a sense that they are nonholonomic deformations with 2+2+2+… and/or (3+1)+(3+1)+.... decompositions of dimensions, encoding nonassociative geometric data, and generalizing the fundamental geometric objects and evolution equations in standard Ricci flow theory.…”

Section: Discussionmentioning

confidence: 99%

“…The originality of nonassociative geometric methods elaborated for the nonholonomic shell oriented structures in refs. [12, 13] consists in developing a formalism which allows us to apply the anholonomic frame and connection method, AFCDM [ 16,17,62 ] for constructing exact and parametric solutions in modified gravity theories, MGTs; see a brief review in Appendix . Using the AFCDM we can prove a general decoupling and integration property of of nonassociative R. Hamilton equations (), see Section 4 and refs.…”

Section: Discussionmentioning

confidence: 99%

“…Following a nonassociative generalized G. Perelman functional formalism, [ 1,7,9–11 ] we can elaborate on a new statistical/ geometric thermodynamic paradigm for classical and quantum gravity and information theories, and study nonlinear models of quasi‐stationary and locally anisotropic cosmological evolution in MGTs, see details in refs. [6–8, 17, 62]. …”

Section: Discussionmentioning

confidence: 99%

“…Here we note that more general examples and various applications for R 2 ‐gravity with locally anisotropic cosmological and BH solutions were studied in ref. [62]. We shall provide explicit proofs of W‐entropy and related formulas for generalized distance and effective massless stated scales for explicit examples of nonassociative BH solutions in next subsections.…”

Section: Extending Swampland Conjectures For Nonassociative Geometric...mentioning

confidence: 99%

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Nonassociative Ricci Flows, Star Product and R‐flux Deformed Black Holes, and Swampland Conjectures

Bubuianu¹,

Vacaru

Veliev

2023

Fortschritte der Physik

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A theory of nonassociative geometric flows is formulated as an extension of a string‐inspired model of nonassociative gravity determined by star product. The nonassociative Ricci tensor and curvature scalar defined by (non) symmetric metric structures and generalized (non) linear connections are used for defining nonassociative versions of Grigori Perelman F‐ and W‐functionals for Ricci flows and computing associated thermodynamic variables. The anholonomic frame and connection deformation method, AFCDM, which allows us to construct exact and parametric solutions describing nonassociative geometric flow evolution scenarios and modified Ricci soliton configurations with quasi‐stationary generic off‐diagonal metrics are developed and applied. There are provided explicit examples of solutions modeling geometric and statistical thermodynamic evolution on a temperature‐like parameter of modified black hole configurations encoding nonassociative star‐product and R‐flux deformation data. Further perspectives of the paper are motivated by nonassociative off‐diagonal geometric flow extensions of the swampland program, related conjectures and claims on geometric and physical properties of new classes of quasi‐stationary Ricci flow and black hole solutions.

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Classical and quantum geometric information flows and entanglement of relativistic mechanical systems

Vacaru

Bubuianu²

2019

Quantum Inf Process

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This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange-Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with methods of computation are developed in general covariant form for curved phase spaces modelled as cotangent Lorentz bundles. The constructions are based on ideas relating the Grigory Perelman's entropy for geometric flows and associated statistical thermodynamic systems to the quantum von Neumann entropy, classical and quantum relative and conditional entropy, mutual information etc. We formulate the concept of the entanglement entropy of quantum geometric information flows and study properties and inequalities for quantum, thermodynamic and geometric entropies characterising such systems. ; the UAIC affiliation is for a hosted IDEI project;

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Geometric flows and Perelman’s thermodynamics for black ellipsoids in R2 and Einstein gravity theories

Cited by 20 publications

References 27 publications

Anamorphic quasiperiodic universes in modified and Einstein gravity with loop quantum gravity corrections

Anamorphic quasiperiodic universes in modified and Einstein gravity with loop quantum gravity corrections

Nonassociative Ricci Flows, Star Product and R‐flux Deformed Black Holes, and Swampland Conjectures

Classical and quantum geometric information flows and entanglement of relativistic mechanical systems

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