Chapter 6. Non-Riemannian Geometry, Born-Infeld Models and Trace Free Gravitational Equations: Mathematical and Physical Consequences

$39.50

Diego Julio Cirilo-Lombardo
University of Buenos Aires, Faculty of Exact and Natural Sciences, Department of Physics, CONICET
National Institute of Plasma Physics (INFIP). Buenos Aires, Argentina
Federal Research Center, Institute of Applied Mathematics, M. V. Keldysh Institute of the Russian Academy of Sciences, Moscow, Russian Federation

Part of the book: Future Relativity, Gravitation, Cosmology

Abstract

Non-Riemannian generalization of the standard Born-Infeld (BI) Lagrangian was recently introduced and analized from a theory of gravitation with dynamical torsion field [14]. The field equations derived from the simplest proposed action lead to a trace free gravitational equation (non-riemannian analog to the trace free equation (TFE) from [1]-[3]) and the field equations for the torsion respectively. In this theoretical context, the fundamental constants arise all from the same geometry through geometrical invariant quantities (as from the curvature R). Important results involving generation of primordial magnetic fields and the link with leptogenesis and baryogenesis that were presented are reviewed and explained. The physically admisible matter fields can be introduced in the model via the torsion vector hµ. Such fields include some dark matter candidates such as axion, right neutrinos and Majorana and moreover, physical observables as vorticity can be included in the same way. From a new wormhole soluton in a cosmological spacetime with torsion we also show that the primordial cosmic magnetic fields can originate from hµ with the axion field (that is contained in hµ) the responsible to control the dynamics and stability of the cosmic magnetic field and the magnetogenesis itself. The analisys of Grand Unified Theories (GUT) in the context of this model indicates that the group manifold candidates are based in SO(10), SU(5) or some exceptional groups as E(6), E (7), etc. High energy astrophysical effects, as the magnetosphere structure of compact objects is reviewed in the same new theoretical context [74]. To this end we show that the new spherically symmetric solution, obtained in this theoretical framework before, physically represents a compact object of pseudoscalar fields (for example, axion field). The axially symmetric version of the Grad-Shafranov equation (GSE) is also derived in this context, and used to describe the magnetosphere dynamics of the obtained ”axion star”. The interplay between high-energy processes and the seed magnetic field with respect to the global structure of the magnetosphere is briefly discussed.


References


[1] David R. Finkelstein, Andrei A. Galiautdinov, James E. Baugh, J. Math. Phys. 42
(2001) 340-346.
[2] George F. R. Ellis, Henk van Elst, Jeff Murugan and Jean-Philippe Uzan, Class.
Quant. Grav. 28 (2011) 225007.
[3] G. Ellis, Gen. Rel. Grav. 46 (2014) 1619.
[4] John Ellis, and Nick E. Mavromatos, Phys. Rev. D88 (2013) no.8, 085029.
[5] Aurelien Barrau and Linda Linsefors, JCAP 12 (2014) 037; Carlos Barcelo, Raul
Carballo-Rubio and Luis J. Garay, Phys. Rev. D89, 124019 (2014); Raul Carballo Rubio, Phys. Rev. D91, 124071 (2015); Javad T. Firouzjaee, George F. R. Ellis Phys.
Rev. D. 91.103002 (2015).
[6] K. Thorne and D. Macdonald, Mon. Not. R. Astron. Soc. 198, 339 (1982).
[7] D. Macdonald and K. Thorne, Mon. Not. R. Astron. Soc. 198, 345 (1982).
[8] D. Kharzeev, Ann. Phys. 325, 2015 (2010).
[9] F. Wilzcek, PRL 58, 1799 (1987).
[10] H. Weyl, “Space-Time-Matter”, Dover (1952).
[11] Yu Xin, 1996, “General Relativity on Spinor-Tensor Manifold”, in: “Quantum Grav ity – Int.School on Cosmology & Gravitation”, XIV Course. Eds. P.G. Bergman, V.
de.Sabbata & H.J. Treder, pp. 382-411, World Scientific.
[12] D.J. Cirilo-Lombardo, Int. J. Theor. Phys. 49, 1288, (2010).
[13] D.J. Cirilo-Lombardo, Int. J. Theor. Phys. 50, 1699 (2011).
[14] D.J. Cirilo-Lombardo, Int. J. Theor. Phys. 50, 3621 (2011).
[15] D.J. Cirilo-Lombardo, J. Math. Phys. 48, 032301, (2007); Class.Quant.Grav. 22 , 4987
(2005).
[16] D.J. Cirilo-Lombardo, Astropart. Phys. 50-52, 51 (2013).
[17] D.J. Cirilo-Lombardo, Int. J. Theor. Phys. 54 (2015) no.10, 3713-3727.
[18] D.J. Cirilo-Lombardo / Journal of High Energy Astrophysics 16 (2017) 1–14
[19] Brett McInnes, Class. Quant. Grav. 1 (1984) 105-113.
[20] Freydoon Mansouri, Phys. Rev. D13 (1976) 3192.
[21] P.M.S. Blackett, Nature 159 (1947), 658.
[22] H. Helmholtz, “Über Integrale der Hydrodynamischen Gleichungen,Welche den
Wirbelbewegungen Entsprechen [About integrals of the hydrodynamic equations,
which correspond to the eddy movements],” J. fürdie reine und angewandte Math ematik, vol. 1858, no. 55, pp. 25-55, Jan. 1858.
[23] H. Helmholtz, “On Integrals of the Hydrodynamical Equations, which Express Vortex Motion,” Philosophical Magazine and J. Science, vol. 33, no. 226, pp. 485-512, 1867.
[24] K.-H. R¨adler and M. Rheinhardt, Geophysical and Astrophysical Fluid Dynamics,
Vol. 101, No. 2, April 2007, 117–154; Diego Julio Cirilo-Lombardo, Int. J. Geom.
Meth. Mod. Phys. 14 (2017) no.07, 1750108.
[25] M.A. Markov, Annals Phys. 155 (1984) 333-357.
[26] David Alvarez-Castillo, Diego Julio Cirilo-Lombardo and Jilberto Zamora-Saa, Solar
neutrinos, helicity effects and new affine gravity with torsion II, JHEAp 13-14 (2017)
10-16.
[27] David Alvarez-Castillo, Diego Julio Cirilo-Lombardo and Jilberto Zamora-Saa, work
in progress.
[28] Albert Einstein, The Meaning of Relativity: Including the Relativistic Theory of the
Non-Symmetric Field, (PUP, Princeton Science Library, 2014).
[29] Edward Kolb and Michael Turner: The Early Universe, Frontiers in Physics (Book
69), Westview Press (February 21, 1994).
[30] M. Joyce, M. Shaposhnikov, Phys. Rev. Lett., 79, 1193 (1997).
[31] Diego Julio Cirilo-Lombardo, Class. Quant. Grav. 22 (2005) 4987-5004.
[32] Green, Schwartz and Witten: Superstring Theory I and II, Cambridge Monogr. Math.
Phys., (Cambridge University Press, 1987).
[33] B. Carter, Commun. Math. Phys. 10, 280 (1968).
[34] K. Yano, Ann. Math. 55, 328 (1952).
[35] V.I. Ogievetsky and I.V. Polubarinov, “Notoph and photon”, preprint JINR P-2330
(1965) (unpublished); V.I. Ogievetsky and I.V. Polubarinov, Soviet J. Nucl. Phys. 4,
156 (1967); M. Kalb and P. Ramond, Phys. Rev. D 9, 2273 (1974).
[36] K.A. Bronnikov and A.M. Galiakhmetov, Grav. Cosmol., 21 (4) 283-288 (2015).
[37] Diego Julio Cirilo-Lombardo, work in preparation.
[38] Pankaj Jain, Gopal Kashyap, and Subhadip Mitra, Int. J. Mod. Phys. A 30, 1550171
(2015).
[39] H.E.S. Velten, R.F. vom Marttens and W. Zimdahl, Eur. Phys. J. C74 (2014) 11, 3160.
[40] S.W. Hawking and G.F.R. Ellis, The large scale structure of spacetime, (Cambridge
University Press, CUP, England, 1973).
[41] Josef Kluson, Phys. Rev. D 91, 064058 (2015).
[42] V. D. Shafranov, Sov. Phys. JETP 6, 545 (1958).;
[43] H. Grad and H. Rubin, in Proceedings of the Second United Nations Conference on
the Peaceful Uses of Atomic Energy (United Nations, Geneva, 1958), Vol. 21, p. 190.
[44] L.S. Solov’ev, Sov. Phys. JETP 26, 400 (1968);
[45] L.E. Zakharov and V. D. Shafranov, Reviews of Plasma Physics (Consultants Bureau,
New York, 1986), Vol. 11, p. 153.
[46] Goldreich, P., and Julian, W. H. 1969, ApJ, 157, 869.
[47] R.V.E. Lovelace, C. Mehanian, C.M., Mobarry, M.E. Sulkanen, 1986, ApJS, 62, 1.
[48] Macdonald, D.A., & Thorne, K.S. 1982, MNRAS, 198, 345.
[49] Okamoto, I. 1975, MNRAS, 173, 357.
[50] D.J. Cirilo-Lombardo, Phys. Part. Nucl. Lett. 14 (2017) no.6, 799-810.
[51] D.J. Cirilo-Lombardo, JHEAp 16 (2017) 1-14.
[52] D.J. Cirilo-Lombardo, Int. J. Geom. Meth. Mod. Phys. 14 (2017) no.07, 1750108.
[53] David Alvarez-Castillo, D. J. Cirilo-Lombardo, Jilberto Zamora-Saa, JHEAp 13-14
(2017) 10-16.
[54] N. Yokoi, Cross helicity and related dynamo, Geophysical & Astrophysical Fluid Dy namics, 107:1-2,(2013) 114-184.
[55] D.J. Cirilo-Lombardo, Astropart. Phys. 50-52 (2013) 51-56.
[56] Maxim Lyutikov, V. I. Pariev and Roger Blandford, Astrophys. J. 597 (2003) 998-1009.
[57] Andrei M. Beloborodov and Christopher Thompson 2007 ApJ 657 967.
[58] Aly, J.J. 1984, ApJ, 283, 349; 1991, ApJ, 375, L61.
[59] D.J. Cirilo-Lombardo, J. Phys. A: Math. and Theor. 45 (2012) 244026.
[60] Vladimir I. Arnold and Boris A. Khesin, Topological Methods in Hydrodynamics,
Applied Mathematical Sciences, Springer Verlag-New York, 1995.
[61] D.J. Cirilo-Lombardo, IJGMMP (online first) doi.org/10.1142/S0219887819500130,
arXiv:1812.04481.
[62] D.J. Cirilo-Lombardo and F.O. Minotti, work in progress.
[63] Yasufumi Kojima, Monthly Notices of the Royal Astronomical Society, Volume 468,
Issue 2, (2017), 2011–2016.
[64] C. Thompson, M. Lyutikov, S.R. Kulkarni, ApJ, 574, 332, (2002).
[65] Friedrich W. Hehl, Paul von der Heyde, G. David Kerlick, and James M. Nester, Rev.
Mod. Phys. 48, 393, (1976).
[66] K. Shibata and T. Magara, Living Reviews in Solar Physics, Volume 8, Issue 1, article
id. 6, 99 pp.
[67] F. Pacini, Nature 219, pages 145–146 (1968).
[68] L Del Zanna and N Bucciantini, MNRAS 479, Issue 1, 657 (2018).
[69] D.J. Cirilo-Lombardo work in progress.
[70] Diego F. Torres, S. Capozziello, G. Lambiase, Phys. Rev. D62 (2000) 104012.
[71] Diego F. Torres, S. Capozziello, G. Lambiase, Class. Quant. Grav. 17 (2000) 3171-3182.
[72] Salvatore Capozziello, Carlo Alberto Mantica and Luca Guido Molinari, IJGMMP,
Vol. 16, No. 01, 1950008 (2019).
[73] Artyom V. Astashenok, Karim Mosani, Sergey D. Odintsov and Gauranga C. Samanta,
online ready: https://doi.org/10.1142/S021988781950035X.
[74] D.J. Cirilo-Lombardo and F.O. Minotti, IJGMMP, Vol. 16, No. 04, 1950064 (2019).
[75] Sraibman, L., Minotti, F. Large-scale Model of the Axisymmetric Dynamo with Feed back Effects. Sol Phys 294, 14 (2019)

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