Advances in Astrophysics

Download PDF (539.6 KB) PP. 136 - 149 Pub. Date: August 1, 2018

DOI: 10.22606/adap.2018.33002

• Magd E. Kahil^*
  Modern Sciences and Arts University, Giza, Egypt; Nile University, Giza, Egypt; Egyptian Relativity Group, Cairo, Egypt

Equations of spinning objects are obtained in Absolute Parallelism Geometry [AP], a special class of non-Riemannian geometry admitting specific types having non-vanishing curvature and torsion simultaneously. This new set of equations is the counterpart of the Papapetrou equations in the Riemannian geometry. Applying, the concept of geometerization of physics, it may give rise to describe the spin tensor as parameterized commutation relation between path and path deviation equations in both Riemannian and non-Riemannian geometries.

Spinning equations, Non-Riemanian geometry ,path equations ,path deviation equations

[1] M. Mathisson, "Neue Mechanik Materireller Systeme" (in German)Acta Phys. Polon , 6, pp163-209 (1937).

[2] A.Papapetrou ,"Spinning Test Particles in General Relativity" ,Proceedings of Royal Society London A, 209 , 248-258(1951).

[3] W. G. Dixon,"Dynamics of Extended Bodies in General Relativity I. Momentum and Angular Momentum",Proc. R. Soc. London, Ser. A, 314, 499-527 (1970).

[4] F. Cianfrani, I. Milillo and G. Montani, "Dixon-Souriau Equations from a 5-dimensional Spinning Particle in a Kaluza-Klein Framework" ,Phys, Lett. A, 366,pp7-13 ; gr-qc/0701157 (2007).

[5] R. Utyiama, Phys Rev., 101 1597 (1956)

[6] T. W. Kibble, Lorentz Invariance and Gravitational Fields , J. Math Phys., 2, pp212-221 (1960)

[7] F.W. Hehl, p. von der Heyde, G.D. Kerlik, and J. M. Nester,"General Relativity with Spin and Torsion: Foundations and Prospects ",Rev Mod Phys 48, pp393-416 (1976)

[8] F.W. Hehl , "Four lectures on Poincare Gauge Field Theory" ,Proceedings of the 6th Course of the International School of Cosmology and Gravitation on "Spin, Torsion and Supergravity", eds. P.G. Bergamann and V. de Sabatta , held at Erice ,pp1-57 (1979).

[9] H.I. Arcos, and J.G. Pereira, Torsion Gravity: A reappraisal : A, International Journal of Modern Physics D ,13, 2193-2240 (2004)

[10] S. Hojman,"Lagrangian Theory of the Motion of Spinning particles in Torsion Gravitational Theories" , Physical Rev. D , 18, pp2741-2744 (1978).

[11] P.H. Yasskin, and W.R. Stoeger, "Propagation Equations of Test Bodies with Spin and Rotation in Theories of Gravity with Torsion",Phys. Rev. D, 21, pp2081-2094(1980).

[12] R. Hammond, "Torsion Gravity", Rep. Prog. Phys, 65, pp599-449 (2002)

[13] K. Hayashi, and T. Shirifuji , "New General Relativity", Phys. Rev. D, 19, pp3524-3553 (1979).

[14] F.I. Mikhail, and M.I. Wanas,"A Generalized Field Theory I. Field Equations" ,Proc. Roy. Soc. Lond. A 356, pp471-481 (1977)

[15] Wanas, M.I.,"Absolute Parallelism Geometry: Developments, Applications, and Problems ", Stud. Cercet. Stiint. Ser. Mat. Univ. Bacau, 10, pp297-309; gr-qc/0209050 (2001).

[16] M.I. Wanas, "Parameterized Absolute Parallelism: A Geometry for Physical Applications" , Turk. J. Phys., 24, 473-488 ; gr-qc/0010099 (2000).

[17] Wanas, M.I., Melek, M. and Kahil, M.E.,"New Path Equations in Absolute Parallelism Geometry", Astrophys. Space Sci.,228, pp273-276. ; gr-qc/0207113 (1995).

[18] Wanas, M.I., "Motion of Spinning Particles in Gravitational fields",Astrophys. Space Sci., 258, pp237-248 ;gr-qc/9904019 (1998).

[19] Wanas, M.I., Melek, M. and Kahil, M.E., "Quantum Interference of Thermal Neutrons and Spin-Torsion Interaction",Grav. Cosmol., 6 , pp319-322 (2000).

[20] Wanas, M.I., Melek, M. and m.E. Kahil, "SN1987A: Temporal Models",Proc. MG IX, part B, pp.1100-1105, Eds. V.G. Gurzadyan et al. (World Scientific Pub.); gr-qc/0306086 (2002).

[21] S.L. Bazanski, "Hamilton-Jacobi Formalism for Geodesics and Geodesic Deviations", J. Math. Phys., 30, 1018-1029 (1989).

[22] M.E. Kahil, Population Dynamics: A Geometrical Approach of Some Epidemic Models ,WSEAS Transaction of Mathematics, 10, issue 12, 454-462 (2011).

[23] D. Bini and A Geralico, Phys. Rev D 84,104012; arXiv: 1408.4952 (2011)

[24] M.E. Kahil, "Motion in Kaluza-Klein Type Theories", J. Math. Physics, 47,052501-050209 (2006).

[25] Magd E. Kahil, "Stability of Stellar Systems orbiting Sgr A*" , Odessa Astronomical Publications, vol 28/2, 126-131 (2015)

[26] Magd E. Kahil, "Spinning and Spinning Deviation Equations for Special Types of Gauge Theories of Gravity",Gravi. Cosmol. 24, 83-90 (2018)

[27] M. Mohseni,"Stability of Circular Orbits of Spinning Particles in Schwarzdschild-Like Space-Times " , Gen. Rel. Grav., 42, 2477-2490 (2010).

[28] M. Roshan, "Test Particle in Modified Gravity",Phys.Rev. D87,044005-... ; arXiv 1210.3136 (2013)

[29] S. C. Ulhosa, and P. M. Rocha , "Neutron Stars in Teleparallel Gravity", Brazilian Journal of Physics, 43, issue 3, pp162-171; arXiv:1206.3675 (2013).