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A Classical Complete Action for a System of Small-Point Massive Charged Particles in General Relativity

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DOI: 10.4236/jmp.2015.610144    3,567 Downloads   3,870 Views  

ABSTRACT

A classical action which describes the motion of a system of small-point massive charged particles including the existence of the electromagnetic and gravitational self-forces, Maxwell equations and Einstein field equations is presented. The action possesses the particularity of being a functional of the variables zi (τi), the trajectory of the i-particle, Aα (x), the electromagnetic 4-potential, and gαβ(x), the metric tensor. It is also considered that the metric tensor gαβ (x) and the potential Aα (x) are not functions of the trajectory of each particle when the variations with respect to the trajectories of the particles are done. That is, the action is complete. The electromagnetic and the gravitational self-forces are analyzed.

Conflicts of Interest

The authors declare no conflicts of interest.

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de Parga, G. and Avalos-Vargas, A. (2015) A Classical Complete Action for a System of Small-Point Massive Charged Particles in General Relativity. Journal of Modern Physics, 6, 1390-1406. doi: 10.4236/jmp.2015.610144.

References

[1] Dirac, P.M. (1938) Proceedings of the Royal Society of London A, 167, 148-169.
http://dx.doi.org/10.1098/rspa.1938.0124
[2] Parrot, S. (1987) Relativistic Electrodynamics and Differential Geometry. Springer, New York.
http://dx.doi.org/10.1007/978-1-4612-4684-8
[3] Spohn, H. (2000) Europhysics Letters, 50, 287-292.
http://dx.doi.org/10.1209/epl/i2000-00268-x
[4] Rohrlich, F. (2000) American Journal of Physics, 68, 1109 -1113.
http://dx.doi.org/10.1119/1.1286430
[5] Rohrlich, F. (2001) Physics Letters A, 283, 276-278.
http://dx.doi.org/10.1016/S0375-9601(01)00264-X
[6] Rohrlich, F. (2007) Classical Charged Particles. Word Scientific Publishing Co., Danvers.
http://dx.doi.org/10.1142/6220
[7] Ares de Parga, G. (2006) Foundations of Physics, 36, 1474-1510.
http://dx.doi.org/10.1007/s10701-006-9072-x
[8] Yaghjian, A.D. (1992) Relativistic Dynamics of a Charged Sphere. Springer, New York.
[9] DeWitt, B.S. and Brehme, R.W. (1960) Annals of Physics, 9, 220-259.
http://dx.doi.org/10.1016/0003-4916(60)90030-0
[10] Hobbs, J.M. (1968) Annals of Physics, 47, 141-165.
http://dx.doi.org/10.1016/0003-4916(68)90231-5
[11] Boulware, D. (1980) Annals of Physics, 124, 169-188.
http://dx.doi.org/10.1016/0003-4916(80)90360-7
[12] Singal, A.K. (1995) General Relativity and Gravitation, 27, 953-967.
http://dx.doi.org/10.1007/BF02113077
[13] Parrot, S. (2002) Foundations of Physics, 32, 407-440.
http://dx.doi.org/10.1023/A:1014861329235
[14] López-Bonilla, J.L. Morales, J. and Rosales, M.A. (1994) Pramana: Journal of Physics, 43, 273-278.
http://dx.doi.org/10.1007/BF02846843
[15] Teitelboim, C. (1971) Physical Review D, 4, 345-347.
http://dx.doi.org/10.1103/PhysRevD.4.345
[16] Plebañski, J. (1972) The Structure of the Field of a Point Charges. Internal report CINVESTAV-IPN, Mexico.
[17] Poisson, E., Pound, A. and Vega, I. (2011) Living Reviews in Relativity, 14, 1-190.
http://dx.doi.org/10.12942/lrr-2011-7
[18] Hadamard, J. (1923) Lectures on Cauchy’s Problem in Linear Partial Differential Equations. Yale University Press, New Haven.
[19] Detweiler, S. and Whiting, B.F. (2003) Physical Review D, 67, Article ID: 024025.
http://dx.doi.org/10.1103/PhysRevD.67.024025
[20] Quinn, T.C. and Wald, R.M. (1997) Physical Review D, 56, 3381-3394.
http://dx.doi.org/10.1103/PhysRevD.56.3381
[21] Mino, Y., Sasaki, M. and Tanaka, T. (1997) Physical Review D, 55, 3457-3476.
http://dx.doi.org/10.1103/PhysRevD.55.3457
[22] Ghosh, S., Choudhury, A. and Sarma, J.K. (2013) Indian Journal of Physics, 87, 607-611.
http://dx.doi.org/10.1007/s12648-013-0254-z
[23] Landau, L.D. and Lifshitz, E.M. (1962) The Classical Theory of Fields. Pergamon, London.
[24] Weinberg, S. (1972) Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. John Wiley & Sons, New York.
[25] Hammond, R.T. (2010) EJTP, 7, 221-258.
[26] Tessarotto, M., Dorigo, M., Cremaschinid, C., Nicolinia, P. and Beklemishev, A. (2008) The Exact Radiation-Reaction Equation for a Classical Charged Particle. arXiv:0807.1819v1.
[27] Galey, C.R., Hu, B.L. and Lin, S.Y. (2006) Physical Review D, 74, Article ID: 024017.
http://dx.doi.org/10.1103/PhysRevD.74.024017
[28] Parrot, S. (2003) Energy Radiation of Charged Particles in Conformally Flat Spacetimes. arXiv:gr-qc/9308023v3.
[29] Kim, D.H. (2005) Radiation Reaction in Curved Spacetime. Ph.D. Thesis, University of Florida, Gainesville.
[30] Geroch, R. and Traschen, J. (1987) Physical Review D, 36, 1017-1031.
http://dx.doi.org/10.1103/PhysRevD.36.1017
[31] McGregor, M.H. (1992) The Enigmatic Electron. Kluer Academic Publishers, Dordrecht.
[32] Barut, A.O. and Zanghi, N. (1984) Physical Review Letters, 52, 2009-2012.
http://dx.doi.org/10.1103/PhysRevLett.52.2009
[33] Ghosh, S., Choudhury, A. and Sarma, J.K. (2012) Apeiron, 19, 247-263.
[34] Ghosh, S., Choudhury, A. and Sarma, J.K. (2012) Indian Journal of Physics, 86, 481-483.
http://dx.doi.org/10.1007/s12648-012-0083-5
[35] Barack, L. (2000) Physical Review D, 62, Article ID: 084027.
http://dx.doi.org/10.1103/PhysRevD.62.084027
[36] Pound, A. and Poisson, E. (2008) Physical Review D, 77, Article ID: 044013.
http://dx.doi.org/10.1103/PhysRevD.77.044013
[37] Vega, I., Wardell, B. and Diener, P. (2011) Classical and Quantum Gravity, 28, Article ID: 134010.
http://dx.doi.org/10.1088/0264-9381/28/13/134010
[38] Gal’tsov, D.V. and Spirin, P.A. (2008) Gravitational Radiation Reaction in Non-Vacuum Space-Time. CAPRA Meeting, Orleans, France, 1-21.
[39] Messaritaki, E. (2003) Radiation Reaction on Moving Particles in General Relativity. Ph.D. Thesis, University of Florida, Gainesville.
[40] Detweiler, S. (2001) Physical Review Letters, 86, 1931-1934.
http://dx.doi.org/10.1103/PhysRevLett.86.1931

  
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