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We develop an axiomatic geometric approach and provide an unconventional review of modified gravity theories, MGTs, with modified dispersion relations, MDRs, encoding Lorentz invariance violations, LIVs, classical and quantum random effects, anisotropies etc.
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S. Vacaru, Critical remarks on Finsler modifications of gravity and cosmology by Zhe Chang and Xin Li, Phys. Lett. B 690 (2010) 224-228; arXiv: 1003.0044v2
2010
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S. Vacaru, New classes of off-diagonal cosmological solutions in Einstein gravity, Int. J. Theor. Phys. 49 (2010) 2753-2776; arXiv: 1003.0043v1
2010
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S. Vacaru, Curve flows and solitonic hierarchies generated by Einstein metrics, Acta Applicandae Mathematicae [ACAP] 110 (2010) 73-107; arXiv: 0810.0707 [math-ph]
2010
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S. Vacaru, Principles of Einstein-Finsler gravity and cosmology, Journal of Physics: Conference Series 314 (2011) 012069; [Proceedings of Spanish Relativity Meeting (ERE 2010): Gravity as a Crossroad in Physics, Granada, Spain, 6-10 September, 2010]; arXiv: 1012. 4148
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Hyun Seok Yang and M. Sivakumar, Emergent gravity from quantized spacetime, Phys. Rev. D82 (2010) 045004, arXiv: 0908.2809
2010
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V. Balan and M. Neagu, Jet Single-Time Lagrange Geometry and Its Applications (Wiley, 2011)
2011
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D. Baleanu and S. Vacaru, Fractional almost Kaehler-Lagrange geometry, Nonlinear Dynamics 64 (2011) 365-373; arXiv: 1006.5535
2011
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D. Baleanu and S. Vacaru, Constant curvature coefficients and exact solutions in fractional gravity and geometric mechanics, Central European Journal of Physics 9 (2011) 1267-1279; arXiv: 1007.2864
2011
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C. Castro, Some consequences of Born’s reciprocal relativity in phase-spaces, IJMPA 26 (2011) 3653-3678
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V. A. Kostelecky, Riemann-Finsler geometry and Lorentz-violating kinematics, Phys. Lett. B 701 (2011) 137-143, arXiv: 1104.5488
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N. E. Mavromatos, Quantum-gravity induced Lorentz violation and dynamical mass generation, Phys. Rev. D 83 (2011) 025018, arXiv: 1011.3528
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C. Pfeifer and M. N. R. Wohlarth, Causal structure and electrodynamics on Finsler spacetimes, Phys. Rev. D 84 (2011) 044039, arXiv: 1104.1079
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C. de Rham, G. Gabadadze and A. J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) 231101, arXiv: 1011.1232
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Z. K. Silagadze, On the Finslerian extension of the Schwarzschild metric, Acta. Phys. Polon. B42 (2011) 1199-1206; arXiv: 1007.4632
2011
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A. Tayebi and E. Peyghan, On a class of Riemannian metrics arising from Finsler structures, C. R. Math. Acad. Sci. Paris 349 (2011) 319-322
2011
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S. Vacaru, On general solutions in Einstein gravity, Int. J. Geom. Meth. Mod. Phys. 8 (2011) 9-21; arXiv: 0909.3949v1
2011
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S. Vacaru, Finsler branes and quantum gravity phenomenology with Lorentz symmetry violations, Class. Quant. Grav. 28 (2011) 215991; arXiv: 1008.4912
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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]
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C. Castro, Gravity in curved phase-spaces, Finsler geometry and two-times physics, IJMPA 27 (2012) 1250069
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Zhe Chang, Sai Wang, Xin Li, Fine structure constant variation or spacetime anisotropy, EPJC 72 (2012) 1838; arXiv: 1106.2726
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V. A. Kostelecky, N. Russel and R. Tso, Bipartite Riemann-Finsler geometry and Lorentz violation, Phys. Lett. B 716 (2012) 470, arXiv: 1209.0750
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C. Laemmerzahl, V. Perlick, and W. Hasse, Observable effects in a class of spherically symmetric static Finsler spacetimes, PRD 86 (2012) 104042, arXiv: 1208.0619
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C. Pfeifer, M. N. R. Wohlarth, Finsler geometric extension of Einstein gravity, PRD 85 (2012) 064009, arXiv: 1112.5641
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M. von Strauss, A. Schmidt-May, J. Enander, E. Mortsell and S. F. Hassan, Cosmological solutions in bimetric gravity and their observational tests, JCAP 1203 (2012) 042, arXiv: 1111/1655
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J. Szilasi and L. Tamassy, Generalized Berwald spaces as affine deformation of Minkowski spaces, Review Roumaine de Mathematiques Pures et Appliquees, 57 (2012) 165-178
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C. Tadmon and S. Plaise Tchapnada, On the spherically symmetric Einstein-Yang-Mills-Higgs equations in Bondi coordinates, Proc. Roy. Soc. Lond. A468 (2012) 3191-3214, arXiv: 1203.3291
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S. Vacaru, Riemann-Finsler and Lagrange gerbes and the Atiyah-Singer theorems, Bulletin of Transilvania University of Brasov. Vol. 5 (54), no. 1 – 2012; Series III: Mathematics, Informatics, Physics (Romania, 2012) 97-128; arXiv: math-ph/0507068
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S. Vacaru, Nonholonomic algebroids, Finsler geometry, and Lagrange-Hamilton spaces, Mathematical Sciences (Springer Open) 6 (2012) 18; arXiv: 0705.0032
2012
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S. Vacaru, Fractional nonholonomic Ricci flows, Chaos, Solitons & Fractals 45 (2012) 1266-1276; arXiv: 1004.0625
2012
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S. Vacaru, Fractional dynamics from Einstein gravity, general solutions, and black holes, Int. J. Theor. Physics 51 (2012) 1338-1359; arXiv: 1004.0628 [math-ph]
2012
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S. Vacaru, Modified dispersion relations in Horava-Lifshitz gravity and Finsler brane models, Gener. Relat. Grav. 44 (2012) 1015-1042; arXiv: 1010.5457
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S. Vacaru, Metric compatible or noncompatible Finsler-Ricci flows, Int. J. Geom. Meth. Mod. Phys. 9 (2012) 1250041; arXiv: 1106.4888
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S. Vacaru, Principles of Einstein-Finsler gravity and perspectives in modern cosmology, Int. J. Mod. Phys. D 21 (2012) 1250072; arXiv: 1004.3007
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S. Vacaru, Wormholes and off-diagonal solutions in f(R,T), Einstein and Finsler gravity theories, in: (eds.) A. Garcia-Parrado, F. C. Mena, F. Moura. E. Vaz, Progress in Mathematical Relativity, Gravitation and Cosmology, Springer Proceedings in Mathematics & Statistics, 60 (2014) 439-443 [Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimaraes, Portugal, September 3-7, 2012], arXiv: 1303.3515v1
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M. S. Volkov, Cosmological solutions with massive gravitons in the bigravity theory, JHEP 1201 (2012) 035, arXiv: 1110.6153
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S. Basilakos, A. P. Kouretsis, E. N. Saridakis, P. Stavrinos, Resembling dark energy and modified gravity with Finsler-Randers cosmology, PRD 88 (2013) 123510, arXiv: 1311.5915
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M. Hohmann, Extensions of Lorentzian spacetime geometry: from Finsler to Cartan and vice versa, Phys. Rev. D 87 (2013) 123034; arXiv: 1304.5430
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J. Klusoň, S. Nojiri and S. D. Odintsov, New proposal for non-linear ghost-free massive F(R) gravity: Cosmic acceleration and Hamiltonian analysis, Phys. Lett. B 726 (2013) 918-925, arXiv: 1309.2185
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N. E. Mavromatos and S. Sarkar, CPT-violating leptogenesis induced by gravitational backgrounds, J, Phys. Conf. Ser. 442 (2013) 012020
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N. E. Mavromatos and S. Sarkar, CPT-violating leptogenesis induced by gravitational defects, EPJC 73 (2013) 2359, arXiv: 1211.0968
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M. Panahi, Hidden connections between general relativity and Finsler geometry, Nuovo. Cim. B118 (2013) 345-351, gr-qc/0312053
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P. Stavrinos and S. Vacaru, Cyclic and ekpyrotic universes in modified Finsler osculating gravity on tangent Lorentz bundles, Class. Quant. Grav. 30 (2013) 055012; arXiv: 1206.3998
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S. Vacaru, Black holes, ellipsoids, and nonlinear waves in pseudo-Finsler spaces and Einstein gravity, Int. J. Theor. Physics 52 (2013) 1654-1681; arXiv: 0905.4401
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S. Vacaru, The algebraic index theorem and Fedosov quantization of Lagrange-Finsler and Einstein spaces, J. Math. Phys. 54 (2013) 073511; arXiv: 1005.3647
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S. Vacaru, Decoupling of Field Equations in Einstein and Modified Gravity, J. Phys.: Conf. Ser. 543 (2013) 012021; arXiv: 1108.2022v3
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N. L. Youssef, A. M. Sid-Ahmed, E. H. Taha, On finslerized absolute parallelism spaces, Int. J. Geom. Meth. Mod. Phys. 10 (2013) 1350029, arXiv: 1206.4505
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G. Amelino-Camelia, L. Barcaroli, G. Gubitosi, S. Liberati and N. Loret, Realization of doubly special relativistic symmetries in Finsler geometries, Phys. Rev. D 90 (2014) 125030; arXiv: 1407.8143
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C. M. Arcus and E. Peyghan, (Pseudo) generalized Kaluza-Klein G-spaces and Einstein equations, Int. J. Math. (2014) 1450116, arXiv: 1406.4122
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C. M. Arcus, E. Peyhgan and E. Saharahi, Weyl’s theory in the generalized Lie algebroid framework, J. Math. Phys. 55 (2014) 123505; arXiv: 1409.2682
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Yu-Fu Cai, F. Duplessis and E. N. Saridakis, F(R) nonlinear massive theories of gravity and their cosmological implications, Phys. Rev. D90 (2014) 045004, arXiv: 1307.7150
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C. Castro, On Clifford space relativity, black hole entropy, rainbow metrics, generalized disperions and uncertainty relations, Found. Phys. 44 (2014) 990-1008
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M. A. Javaloyes and M. Sanchez, Finsler metrics and relativistic spacetimes, IJGMMP 11 (2014) 1460032, arXiv: 1311.4770
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T. Gheorghiu, O. Vacaru and S. Vacaru, Off-diagonal deformations of Kerr black holes in Einstein and modified massive gravity and Higher Dimensions, Eur. Phys. J. C 74 (2014) 3152; arXiv: 1312.4844
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A. P. Kouretsis, M. Stathakopoulos, and P. C. Stavrinos, Relativistic Finsler geometry, Math. Meth. Appl. Sci. 37 (2014) 223-229
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X. Li and Z. Chang, Exact solution of vacuum field equation in Finsler spacetime, PRD, 90 (2014) 064049, arXiv: 1401.6363
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Xin Li, Sai Wang, and Zhe Chang, Finslerian perturbation for the Λ \Lambda CDM model, Commun. Theor. Physics, 61 (2014) 781-788, arXiv: 1309.1758
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Kai Lin, A spherical symmetrical spacetime solution in Finsler gravity, IJTP 53 (2014) 1271-1275
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B. Russell and S. Stepney, Zermelo navigation and a speed limit to quantum information processing, Phys. Rev. A 90 (2014) 012303, arXiv: 1310.6731
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P. Stavrinos, O. Vacaru and S. Vacaru, Off-diagonal solutions in modified Einstein and Finsler theories on tangent Lorentz bundles, Int. J. Mod. Phys. D 23 (2014) 1450094; arXiv: 1401.2879
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S. Vacaru, Covariant renormalizable modified and massive gravity theories on (non) commutative tangent Lorentz bundles, Int. J. Geom. Meth. Mod. Phys. 11 (2014) 1450032; arXiv: 1304.1079
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S. Vacaru, Exact solutions in modified massive gravity and off-diagonal wormhole deformations, Eur. Phys. J. C 74 (2014) 2781; arXiv: 1403.1815
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S. Vacaru, Ghost-free massive f(R) theories modelled as effective Einstein spaces & cosmic acceleration, Eur. Phys. J. C 74 (2014) 3132; arXiv: 1401.2882
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S. Vacaru, E. Veli Veliev and Enis Yazici, A geometric method of constructing exact solutions in modified f(R,T) gravity with Yang-Mills and Higgs Interactions, Int. J. Geom. Meth. Mod. Phys. 11 (2014) 1450088; arXiv: 1411.2849
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Q. G. Bailey, V. A. Kostelecky, and Rui Xu, Short-range gravity and Lorentz violation, PRD 91 (2015) 022006, arXiv: 1410.6162
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E. Elizalde and S. Vacaru, Einstein spaces modeling modified gravity, Eur. Phys. J. Plus 130 (2015) 119, arXiv: 1506.09148
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J. Foster and R. Lehnert, Classical-hysics applications for Finsler b spaces, Phys. Lett. B746 (2015) 164-170, arXiv: 1504.07935
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T. Gheorghiu, O. Vacaru and S. Vacaru, Modified dynamical supergravity breaking and off-fiagonal super-Higgs effects, Class. Quant. Grav. 32 (2015) 065004; arXiv: 1311.6365
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E. Minguzzi, Light cones in Finsler spacetime, Comm. Math. Phys. 334 (2015) 1529-1551, arXiv: 1403.7060
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E. Minguzzi, Raychaudhuri equation and singularity theorems in Finsler spacetimes, CQG 32 (2015) 185008, arXiv: 1502.02313
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F. Rahman, N. Paul, S. S. De, Saibal Ray and Md. Abdul Kayum Jafry, The Finslerian compact star model, EPJC 75 (2015) 564, arXiv: 1506.02501
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S. Rajpoot and S. Vacaru, Black Ring and Kerr Ellipsoid – Solitonic Configurations in Modified Finselr Gravity, Int. J. Geom. Meth. Mod. Phys. 12 (2015) 1550102; arXiv: 1506.08696
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G. Rosati, G. Amelino-Camelia, A. Marciano and M. Matassa, Planck-scale-modified dispersion relations in FRW spaceteime, Phys. Rev. D 92 (2015) 124042; arXiv: 1507.02056
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M. Schreck, Eikonal approximation, Finsler structures, and implications for Lorentz-violating phonons in weak gravitational fields, PRD 92 (2015), arXiv: 1508.00216
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S. Vacaru, Cosmological solutions in biconnection and bimetric gravity theories, in: On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories (in 3 volumes); Proceedings of the Tirteenth Marcel Grossmann Meeting on General Relativity, Stockholm University, Sweden, 1-7 July 2012 (World Scientific, 2015), pp. 1276-1278, arXiv: 1304.2916
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S. Vacaru, Almost Kaehler Ricci flows and Einstein and Lagrange-Finsler structures on Lie algebroids, Medit. J. Math. 12 (2015) 1397-1427; arXiv: 1306.2813
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S. Vacaru, Spinors and Twistor Geometry in Einstein Gravity and Finsler Modifications, Advances in Applied Clifford Algebras 25 (2015) 453-485; arXiv: 1206.4012
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A. B. Aazami and M. A. Javaloyes, Penrose’s singurlarity theorem in a Finsler spacetime, Class. Quant. Grav. 33 (2016) 025003, arXiv: 1410.7595
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E. Caponio and G. Stancarone, Standard static Finsler spacetimes, IJGMMP 13 (2016) 1650040; arXiv: 1506.07451
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C. Castro, A gauge theory of gravity in curved-phase-spaces, IJGMMP 13 (2016) 1650097
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M. Hohmann, Spacetime and observer space symmetries in the language of Cartan geometry, J. Math. Phys. 57 (2016) 082502, arXiv: 1505.07809
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T. Gheorghiu, V. Ruchin, O. Vacaru and S. Vacaru, Geometric flows and Perelman’s thermodynamics for black ellipsoids in R2 and Einstein gravity theories; Annals of Physics, NY, 369 (2016) 1-35; arXiv: 1602.08512
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M. Kontsevich, Deformation quantizationof Poisson manifolds, I. Latt. Math. Phys. 66 (2003) 157-2016, arXiv: q-alg/9709040
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Xin Li and Sai Wang, Primordial power spectrum of tensor perturbations in Finsler spacetime, EPJC 76 (2016) 51, arXiv: 1508.04331
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E. Minguzzi, An equivalence of Finslerian relativistic theories, Rep. Math. Phys. 77 (2016) 45-55, arXiv: 1412.4228
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F. Rahman, N. Paul, A. Banerjee, S. S. De, S. Ray and A. A. Usmani, The Finslerian wormhole models, EPJC 76 (2016), 246; arXiv: 1607.04329
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M. Schreck, Classical Lagrangians and Finsler structures for the nonminimal fermion sector of the Standard-Model extension, PRD 93 (2016) 10517, arXiv: 1512.04299
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M. Schreck, From classical Lagrangians to Hamilton operators in the Standard-Model extension, PRD 94 (2016) 025019, arXiv: 1602.01527
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S. Vacaru, Noncommutative Einstein, almost Kaehler – Finsler and Quantum Deformations. Chapter 24 in: “The Algebraic Way. Space, Time and Quantum Beyond Peaceful Coexistence”, ed. Ignazio Licata (World Scientific, Singapore, 2016), pp. 661-695
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S. Vacaru, Off-Diagonal Ekpyrotic Scenarios and equivalence of modified, massive and/or Einstein gravity, Phys. Lett. B 752 (2016) 27-33; arXiv: 1304.1080
2016
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M. M. Amaral, R. Aschheim, L. Bubuianu, K. Irwing, S. Vacaru, and D. Woolridge, Anamorphic quasiperiodic universes in modified and Einstein gravity with loop quantum gravity corrections, Class. Quant. Grav. 34 (2017) 185002, arXiv: 1611.05295
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A. N. Bernal, B. Janssen, A. Jimenez-Cano, J. A. Orejuela, M. Sanchez, and P. Sanchez-Moeno, On the (non-) uniqueness of the Levi-Civita solution in the Einstein-Hilbert-Palatiny formalism, Phys. Lett. B768 (2017) 280-287, arXiv: 1606.08756
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L. Bubuianu, K. Irwin and S. Vacaru, Heterotic supergravity with internal almost-Kaehler spaces; instantons for SO(32), or E8 x E8, gauge groups; and deformed black holes with soliton, quasiperiodic and/or pattern-forming structures, Class. Quant. Grav. 34 (2017) 075012; arXiv: 1611.00223
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G. Calcangi, Multifractional theories: an unconventional review, JHEP 1703 (2017) 138, Erratum: JHEP 1706 (2017) 020, arXiv: 1612.05632
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R. Gallego Torrome, On singular generalized Berwald spacetimes and the equivalence principle, IJGMMP 13 (2017) 1750091; arXiv: 1606.07469
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I. P. Lobo, N. Loret and F. Nettel, Investigation on Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case, Phys. Rev. D 95 (2017) 046015. arXiv: 1611.04995
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E. Minguzzi, Affine spher spacetimes which satisfy the relativity principle, Phys. Rev. D95 (2017) 024019, arXiv: 1702.06475
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S. Rajpoot and S. Vacaru, On supersymmetric geometric flows and R2 inflation from scale invariant supergravity, Annals of Physics, NY, 384 (2017) 20-60; arXiv: 1606.06884
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S. Rajpoot and S. Vacaru, Nonholonomic Jet Deformations, Exact Solutions for Modified Ricci Soliton and Einstein Equations, Int. J. Geom. Meth. Mod. Phys. 14 (2017) 1750032, arXiv: 1411.1861 [math-ph]
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J. A. A. A. S. Reis and M. Schreck, Lorentz-violating modifiecation of Dirac tehory bases on spin-nondegenerate operators, Phys. Rev. D 95 (2017) 075016, arXiv: 1612.06221
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V. Ruchin, O. Vacaru and S. Vacaru, Perelman’s W-entropy and statistical and relativistic thermodynamic description of gravitational fields, Eur. Phys. J. C 77 (2017) 184; arXiv: 1312.2580
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S. Vacaru and K. Irwin, Off-diagonal deformations of Kerr metrics and black ellipsoids in heterotic supergravity, Eur. Phys. J. C 77 (2017) 17; arXiv: 1608.01980
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N. Voicu, Volume forms for time orientable Finsler spacetimes, J. Geom. Phys. 112 (2017) 85-94, arXiv: 1507.00847
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M. A. Wasay and S. Bashir, Two particle entaglement in its geometric duals, Eur. Phys. J. C 77 (2017) 77, arXiv: 1708.03164
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S. Vacaru, Diffusion and self-organized criticality in Ricci flow evolution of Einstein and Finsler spaces, SYMMETRY: Culture and Science, vol. 23, nr. 2, (2013) 105-124; ISSN 0865-4824 (printed), ISSN 2226-1877 (online), Thematic Issue: Field theories on Finsler Space (Symmetries with Finsler metric, 2013); arXiv: 1010.2021
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S. Vacaru, Covariant renormalizable anisotropic theories and off-diagonal Einstein-Yang-Mills-Higgs solutions, Europhysics Letters (EPL) 96 (2011) 50001; arXiv: 1108.2023
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S. F. Hassan and R. A. Rosen, Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity, JHEP 1204 (2012) 123, arXiv: 1111.2070
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