05 Vacaru Raport Stiintific IDEI 2012

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Raport stiintific (Scientific Report)

privind implementarea proiectului in perioada ianuarie decembrie 2012

(on ProjectIDEI, PN-II-ID-PCE-2011-3-0256, December 2012 ) (max 5pages)

Summary: There are reported 11 published scientific works: seven main high influent

score/ ISI articles [1-7] published and listed in ISI Web of Knowledge in 2012; four online

and proceeding type articles at Springer (two of them listed in MathSciNet) and a paper in

Romania (see works [8-11]). We list this year four electronic preprints [12p-15p] submitted

to Editors. Project funds were used for complete or partial support (together with hosts

accommodations) of six scientific visits in Greece, Poland, Sweden, Estonia, Portugal and

Turkey for nine invited talks/seminars; 4 communications at Conferences/Seminars in

Romania (2 of them being International), see details from the list of13 communications in

[1c-13c], where the scientific results of the Project were communicated and futurecollaborations were established. We applied 3 soft programs and two performance laptops

and other relevant equipment got in 2012 using Projects funds and necessary for numeric,

analytic and graphic performing of scientific works and communications.

Remarks: 1. Published/ submitted articles and talks are relevant to the Objectives of this Project on

Geometric Methods in Gravity and Nonlinear Dynamics. Here we emphasize that it may take

more than 12 months (for math physics and theoretical physics journals) and more than 24 months

(for math journals) till a paper is reviewed and published. After reduction with 10% of the funds for

the prosed 3 years Project, the team signed the obligation to publish at least 12 (maximum 15) highinfluence score/ high ISI impact papers. During 14 months in 2011-2012, we reported 11 such

publications. Other ones, at least 1-4, are planned for 2013-2014. Similar numbers of

communications/ participations at International Conferences/Seminars were reported

correspondingly for 2011, 2012 and will be planned for 2013, 2014.

2. We provide the Titles and shorten Abstracts of seven main ISI articles [1-7] with links in the

Web. The complete Scientific Report consists from Sections 1 and 2 (with relevant information on

preprints, conferences etc). This Report is provided in English because a) the Proposal was in English

and evaluated by exterior referees, b) all publications and talks were in English and c) there is notan established terminology in Romanian on such new directions of mathematical physics.

Section 1. Titles and Abstracts of Main ISI Publications [1-11]

Subsection 1a: Main Articles in high influent score/impact journals [1-6] and [7]

Main Paper [1]. S. Vacaru, Covariant renormalizable anisotropic theories and off-diagonal

Einstein-Yang-Mills-Higgs solutions, Europhysics Letters (EPL) 96 (2011) 50001; arXiv:

1108.2023 [published by December 20, 2011 and put in ISI Web of Knowledge in March, 2012; this red

paper was granted 4000 Ron in April 2012 in the competition of scientific works; it was not possible to

report it on December 15, 2011]


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DOI:10.1209/0295-5075/96/50001 ; Abstract: We use an important decoupling property of gravitational

field equations in the general relativity theory and modifications, written with respect to nonholonomic

frames with 2+2 spacetime decomposition. This allows us to integrate the Einstein equations (eqs) in very

general forms with generic off-diagonal metrics depending on all spacetime coordinates via generating and

integration functions containing (un-)broken symmetry parameters. Finally, we show how the

constructions can be extended to include exact solutions for conjectured covariant reonormalizable

models with Einstein-Yang-Mills-Higgs fields.

Main Paper [2]. S. Vacaru, Modified Dispersion Relations in Horava-Lifshitz Gravity and

Finsler Brane Models, Gener. Relat. Grav. 44 (2012) 1015-1042; arXiv: 1010.5457 [there is a

November 2012 application for this paper to be granted 2000 Ron in the competition of scientific works]

DOI: 10.1007/s10714-011-1324-1; Abstract: We study possible links between quantum gravity

phenomenology encoding Lorentz violations as nonlinear dispersions, the EinsteinFinsler gravity models,

EFG, and nonholonomic (non-integrable) deformations to HoravaLifshitz, HL, and/or Einsteins general

relativity, GR, theories. EFG and its scaling anisotropic versions formulated as HoravaFinsler models, HF,

are constructed as covariant metric compatible theories on (co) tangent bundle to Lorentz manifolds and

respective anisotropic deformations. Such theories are integrable in general form and can be quantized

following standard methods of deformation quantization, A-brane formalism and/or (perturbatively) as a

nonholonomic gauge like model with bi-connection structure.

Main Paper [3]. S. Vacaru, Fractional Nonholonomic Ricci Flows, Chaos, Solitons & Fractals

45 (2012) 1266-1276; arXiv: 1004.0625 [there is a November 2012 application for this paper to be

granted 2000 Ron in the competition of scientific works]

DOI: http://dx.doi.org/10.1016/j.chaos.2012.06.011; Abstract: We formulate the fractional Ricci flow

theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional

integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of

Perelmans functionals and derived the corresponding fractional evolution (Hamiltons) equations.

Main Paper [4]. S. Vacaru, Metric Compatible or Noncompatible Finsler-Ricci Flows, Int. J.

Geom. Meth. Mod. Phys. 9 (2012) 1250041 (26 pages); arXiv: 1106.4888 [high influent

score/impact journal].

DOI: 10.1142/S0219887812500417 ; Abstract: There were elaborated different models of Finslergeometry using the Cartan (metric compatible), or Berwald and Chern (metric non-compatible)

connections, the Ricci flag curvature, etc. In a series of works, we studied (non)-commutative metric

compatible Finsler and non-holonomic generalizations of the Ricci flow theory [see S. Vacaru, J. Math.

Phys. 49 (2008) 043504; 50 (2009) 073503 and references therein]. The aim of this work is to prove that

there are some models of Finsler gravity and geometric evolution theories with generalized Perelmans

functionals, and correspondingly derived non-holonomic Hamilton evolution equations, when metric non-

compatible Finsler connections are involved.

Main Paper [5]. S. Vacaru, Principles of Einstein-Finsler Gravity and Perspectives in ModernCosmology, Int. J. Mod. Phys. D 21 (2012) 1250072 (40 pages); arXiv: 1004.3007 [high
http://dx.doi.org/10.1016/j.chaos.2012.06.011http://dx.doi.org/10.1016/j.chaos.2012.06.011http://dx.doi.org/10.1016/j.chaos.2012.06.011


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influent score/impact journal; this paper was scheduled for publication in 2013 but certain prompt

Editorial activity allowed to obtain visibility in ISI Web of Knowledge for November 2012].

DOI: 10.1142/S0218271812500721 ; Abstract: We study the geometric and physical foundations of Finsler

gravity theories with metric compatible connections defined on tangent bundles, or (pseudo) Riemannian

manifolds, endowed with nonholonomic frame structure. Several generalizations and alternatives to

Einstein gravity are considered, including modifications with broken local Lorentz invariance. It is also

shown how such theories (and general relativity) can be equivalently re-formulated in Finsler like variables.

Main Paper [6]. S. Vacaru, Fractional Dynamics from Einstein Gravity, General Solutions,

and Black Holes, Int. J. Theor. Physics51 (2012) 1338-1359; arXiv: 1004.0628

DOI: 10.1007/s10773-011-1010-9 ; Abstract: We study the fractional gravity for spacetimes with non-

integer fractional derivatives. Our constructions are based on a formalism with the fractional Caputo

derivative and integral calculus adapted to nonholonomic distributions. This allows us to define a fractional

spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all

being similar to respective integer dimension constructions. Such models of fractional gravity mimic theEinstein gravity theory and various LagrangeFinsler and HamiltonCartan generalizations in nonholonomic

variables.

Main Paper [7]. S. Vacaru, Nonholonomic Relativistic Diffusion and Exact Solutions for

Stochastic Einstein Spaces, The European Physical Journal Plus, 127 (2012) 32 (22 pages);

ISNN 2190-5444 (electronic), Journal no. 13360; arXiv: 1010.0647 [math-ph]

DOI 10.1140/epjp/i2012-12032-0 ; Abstract: We develop an approach to the theory of nonholonomic

relativistic stochastic processes in curved spaces. The Ito and Stratonovich calculus are formulated forspaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting defined by nonlinear

connection structures. Geometric models of the relativistic diffusion theory are elaborated for

nonholonomic (pseudo) Riemannian manifolds and phase velocity spaces.

Subsection 1b: Articles published in Springer online journals and proceedings and in

a journal of Transilvania University of Brasov, Romania; there is not enough room in this

Report to present all abstracts of such papers but we provide the corresponding links in Internet

and/or numbers of some papers/ reviews in MathSciNet), see [8-11]:

[8]. S. Vacaru, Nonholonomic Algebroids, Finsler Geometry, and Lagrange-Hamilton Spaces,

Mathematical Sciences (Springer) 2012, 6:18;http://www.iaumath.com/content/6/1/18/abstract ;

arXiv: 0705.0032 [math-ph]

[9]. D. Baleanu and S. Vacaru, Fractional analogous models in mechanics and gravity

theories, in: Fractional Dynamics and Control, Part 3, editors: D. Baleanu, J. A. Tenreiro

Machado and A. Luo (Springer, 2012), pages 199-207, ISBN 978-1-4614-0456-9; arXiv:

1008.0363 [math-ph]; indexed in MathSciNet: MR2905877
http://www.iaumath.com/content/6/1/18/abstracthttp://www.iaumath.com/content/6/1/18/abstracthttp://www.iaumath.com/content/6/1/18/abstracthttp://www.iaumath.com/content/6/1/18/abstract


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[10]. D. Baleanu and S. Vacaru, Fractional exact solutions and solitons in gravity, in:

Fractional Dynamics and Control, Part 3, editors: D. Baleanu, J. A. Tenreiro Machado and A.

Luo (Springer, 2012), pages 229-236, ISBN 978-1-4614-0456-9; arXiv: 1008.0360 [math-ph];

indexed in MathSciNet: MR2905880

[11]. S. Vacaru, Riemann-Finsler and Lagrange Gerbes and the Atiyah-Singer Theorems,

Bulletin of Tansilvania University of Brasov. Vol. 5 (54), no. 1 2012; Series III:

Mathematics, Informatics, Physics (Romania, 2012) 97-128; arXiv: math-ph/0507068;

http://webbut.unitbv.ro/bulletin/Series%20III/BULETIN%20III%20PDF/vacaru%202012.pdf

Section 2. All Relevant Electronic Preprints, Seminars, Lectures and Conferences

Subsection 2a: Electronic Preprints (submitted to Editors; they will be reported in final

form in 2013-2014), numbered 1p, 2p, (p from preprint)

12p. M. Anastasiei, Selected Papers, 304 pages, arXiv: 1202.6202v2 [math.DG], 28 Sep 2012

13p. S. Vacaru, Finsler Spinors and Twistors in Einstein Gravity and Modifications, arXiv:

1206.4012 [math-ph]

14p. P. Stavrinos and S. Vacaru, Cyclic and Ekpyrotic Universes in Modified Finsler

Osculating Gravity on Tangent Lorentz Bundles, arXiv: 1206.3998 [astro-ph.CO]

15p. S. Vacaru, Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci

Flows, and Mathematical Relativity [habilitation thesis], arXiv: 1204.5387 [math-ph]

Subsection 2b: International Conferences/Seminars/ Lectures [a series of relevant papers

will published in Proceedings in 2013-2014 when such works will be finally reported] numbered 1c,

2c, (c from conference etc)

1c. M. Anastasiei, Banach Lie algebroids and Dirac structures. 30 min. Commuication at: The V-th

International Conference of Differential Geometry and Dynamical Systems (DGDS-2012), 29 Aug -30 Sept,

2012; Mangalia, Romania;http://www.mathem.pub.ro/dept/dgds-12/DGDS-12.htm

2c. S. Vacaru, QCD and Modified Gravity, invited talk/ short visit during 25-30 November, 2012, Kocaely

University, Turkey (partial support by host and project IDEI)

3c. S. Vacaru, Questions and Problems on Methodology an Habilitation on Mathematical Physics,

Conference: Diaspora in Cercetarea Stiintifica si Invatamantul Superior din Romania, Bucuresti, 25-28

septembries 2012; Workshop 6. Fizica la marile colaborari internationale, 27 septembrie, 2012 [20 minits]

4c. S. Vacaru, Dirac Operators and (Non) Commutative Finsler Ricci Flows and Mathematical Relativity, oral

communication at commission for a CS1 position (the Romanian equivalent for research professor),

Department of Science, Alexandru Ioan Cuza University, UAIC, Iasi, Romania, September 17, 2012
http://webbut.unitbv.ro/bulletin/Series%20III/BULETIN%20III%20PDF/vacaru%202012.pdfhttp://webbut.unitbv.ro/bulletin/Series%20III/BULETIN%20III%20PDF/vacaru%202012.pdfhttp://www.mathem.pub.ro/dept/dgds-12/DGDS-12.htmhttp://www.mathem.pub.ro/dept/dgds-12/DGDS-12.htmhttp://www.mathem.pub.ro/dept/dgds-12/DGDS-12.htmhttp://www.mathem.pub.ro/dept/dgds-12/DGDS-12.htmhttp://webbut.unitbv.ro/bulletin/Series%20III/BULETIN%20III%20PDF/vacaru%202012.pdf


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5c. S. Vacaru, Wormhole Off-Diagonal Solutions in f(R,T), Einstein and Finsler Gravity Theories, Oral

Communication (September 6), Section IV-B, ERE 2012; Spanish Relativity Meeting in Portugal,

Universidade do Minho, Portugal, Guimaraes, September 3-7, 2012

6c. S. Vacaru, Perspective si probleme in realizarea Proiectului IDEI la UAIC, in 2012, si ulterior. Sedinta de

Seminarii, Departament Stiinte, UAIC, 20 iulie 2012 [10 min]

7c. S. Vacaru, (Non) Commutative Ricci Solitonic Hierarchies and Deformation Quantization, OralCommunication (July 12), Conference: 3 Quantum: Algebra, Geometry, Information, Tallinn University of

Technology, Estonia; July 10-14, 2012

8c. S. Vacaru, Generic Off-Diagonal Solutions and Solitonic Hierarchies in Einstein and Modified Gravity,

Oral Communication (July 6), Parallel Section GT1 Exact Solutions in Four and Higher Dimensions:

Mathematical Aspects; Thirteen Marcel Grossmann Meeting MG13, Stockholm University, Sweden; July

1-7, 2012

9c. S. Vacaru, Cosmological Solutions in Biconnection and Bimetric Gravity Theories, Oral Communication

(July 5), Parallel Section AT4a Modified Gravity; Thirteen Marcel Grossmann Meeting MG13, Stockholm

University, Sweden; July 1-7, 2012

10c. S. Vacaru, Covariant Renormalizable Gravity Theories on (Non) Commutative Tangent Bundles, Oral

Communication (July 3), Parallel Section QG2b Quantum Gravity Phenomenology; Thirteen Marcel

Grossmann Meeting MG13, Stockholm University, Sweden; July 1-7, 2012

11c. S. Vacaru, Noncommutative almost Kaehler Ricci solitons and deformation quantization, talk at XXXI

Workshop on Geometric Methods in Physics, Biaowieza, Poland, June 24-30, 2012

12c S. Vacaru, Decoupling of Field Equations in Einstein and Modified Gravity, talk at Session B, on June 22,

2012; Conference "Recent Developments in Gravity - NEB15", June 20 - 23, 2012, Chania, GREECE,

Hellenic Society on Relativity, Gravitation and Cosmology

13c. S. Vacaru, Finsler Methods and Exact Solutions in Einstein and Modified Gravity, Survey Lecture at

Department of Mathematics, University of Athens, on June 15, 2012, with a research/ seminar visit during

13 - 18 June, 2012, Greece

Projects Director,

Sergiu Vacaru ______________

05 Vacaru Raport Stiintific IDEI 2012

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