Abstract
The goal of this paper is to link the geometric variables of strain gradient continuum with electromagnetic fields. For that purpose, we derive the electromagnetic wave equation within a Riemann-Cartan continuum where curvature and torsion are present. We also show that the gravitational and electromagnetic fields are respectively identified as geometric objects of such a continuum, namely the curvature \( \Re_{\alpha \beta \lambda }^{\gamma } \) for gravitation which is a classical result, and the torsion \( \aleph_{\alpha \beta }^{\gamma } \) as source of electromagnetism.
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References
Antonio Tamarasselvame N, Rakotomanana L (2011) On the form-invariance of Lagrangean function for higher gradient continuum. In: Altenbach H, Maugin GA, Erofeev V (eds) Mechanics of Generalized Continua, Heidelberg, ASM, vol 7, pp 291–322
Charap JM, Duff MJ (1977) Gravitational effects on Yang-Mills topology. Physics Letters 69B(4):445–447
Cho YM (1976) Einstein Lagrangian as the translational Yang-Mills Lagrangian. Physical Review D 14(10):2521–2525
de Andrade VC, Pereira JG (1999) Torsion and the electromagnetic field. International Journal of Modern Physics D 8(2):141–151
Dias L, Moraes F (2005) Effects of torsion on electromagnetic fields. Brazilian Journal of Physics 35(3A):636–640
Fernado J, Giglio T, Rodrigues Jr WA (2012) Gravitation and electromagnetism as geometrical objects of Riemann-Cartan spacetime structure. Advanced Applied Clifford Algebras 22:640–664
Fernandez-Nunez I, Bulashenko O (2016) Anisotropic metamaterial as an anlogue of a black hole. Physics Letters A 380:1–8
Fumeron S, Pereira E, Moraes F (2015) Generation of optical vorticity from topological defects. Physica B 476:19–23
Futhazar G, Le Marrec L, Rakotomanana LR (2014) Covariant gradient continua applied to wave propagation within defected material. Archive for Applied Mechanics 84(9–11):1339–1356
Hammond RT (1987) Gravitation, Torsion, and Electromagnetism. General Relativity and Gravitation 20(8):813–827
Hammond RT (1989) Einstein-Maxwell theory from torsion. Classical Quantum and Gravitation 6:195–198
Hehl FW (2008) Maxwell’s equations in Minkowski’s world: their premetric generalization and the electromagnetic energy-momentum tensor. Annalen der Physik 17(9-10):691–704
Hehl FW, von der Heyde P (1973) Spin and the structure of spacetime. Annales de l’Institut Henri Poincaré, section A 19(2):179–196
Hehl FW, von der Heyde P, Kerlick JM G D ans Nester (1976) General relativity with spin and torsion: Foundations and prospects. Reviews of Modern Physics 48(3):393–416
Kleinert H (2008) Multivalued Fields: in Condensed matter, Electromagnetism, and Gravitation. World Scientific, Singapore
Kovetz A (2000) Electromagnetic Theory. Oxford University Press, Oxford
Maugin G (1993) Material Inhomogeneities in Elasticity. Chapman and Hall, London
Maugin GA (1978) Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids. Annales de l’Institut Henri Poincaré, section A 28(2):155–185
Milonni PW, Boyd RW (2010) Momentum of light in a dielectric medium. Adv Opt Photon 2(4):519–553
Obukhov YN (2008) Electromagnetic energy and momentum in moving media. Annalen der Physik 17(9-10):830–851
Obukhov YN, Hehl FW (2003) Electromagnetic energy-momentum and forces in matter. Physics Letters A 311:277–284
Plebanski J (1960) Electromagnetic waves in gravitational fields. Physical Review 118(5):1396–1408
Poplawski NJ (2010) Torsion as electromagnetism and spin. International Journal of Theoretical Physics 49(7):1481–1488
Prasanna AR (1975) Maxwell’s equations in Riemann-Cartan space U 4. Physics Letters A 54(1):17–18
Puntigam RA, Lämmerzahl C, Hehl FW (1997) Maxwell’s theory on a post-Riemannian spacetime and the equivalence principle. Classical and Quantum Gravitation 14:1347–1356
Rakotomanana RL (2003) A Geometric Approach to Thermomechanics of Dissipating Continua. Progress in Mathematical Physics Series, Birkhaüser, Boston
Schutzhold R, Plunien G, Soff G (2002) Dielectric black hole analogs. Physical Review Letters 88(6):061,101/1–061,101/4
Smalley LL (1986) On the extension of geometric optics from Riemaniann to Riemann-Cartan spacetime. Physics Letters A 117(6):267–269
Smalley LL, Krisch JP (1992) Minimal coupling of electromagnetic fields in Riemann-Cartan spacetimes for perfect fluids with spin density. Journal of Mathematical Physics 33(3):1073–1081
Sotiriou TP, Liberati S (2007) Metric-affine f (R) theories of gravity. Annals of Physics 322:935–966
Tiwari RN, Ray S (1997) Static spherical charged dust electromagnetic mass models in Einstein- Cartan theory. General Relativity and Gravitation 29(6):683–690
Vandyck MA (1996) Maxwell’s equations in spaces with non-metricity and torsion. J Physics A : Math Gen 29:2245–2255
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Rakotomanana, L.R. (2018). Second Gradient Continuum: Role of Electromagnetism Interacting with the Gravitation on the Presence of Torsion and Curvature. In: Altenbach, H., Pouget, J., Rousseau, M., Collet, B., Michelitsch, T. (eds) Generalized Models and Non-classical Approaches in Complex Materials 1. Advanced Structured Materials, vol 89. Springer, Cham. https://doi.org/10.1007/978-3-319-72440-9_36
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DOI: https://doi.org/10.1007/978-3-319-72440-9_36
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