Action Functional of the Electomagnetic Field: Effect of Gravitation
The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.
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[5] Harish Parthasarathy, Advanced Engineering Physics, First Edition , Ane
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[6] A. Vaish and H. Parthasarathy, Finite Element Analysis of Propagation
Modes in a Waveguide: Effect of Gravitational Field, Accepted for
publication in HAIT journal of Engineering and Science, 2007.
[7] D. F. Lawden, An Introduction to Tensor Calculus, Relativity and Cosmology,
Third Edition , Chapman and Hall Ltd, London, 1986.
[8] Cheng and Ta-Pei , Relativity, Gravitation and Cosmology- a Basic
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[9] Hartle and James B, Gravity: an Introduction to Einstein-s General
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Finite Element Method, Communicated, 2007.
[18] J. H. Heinbockel, Introduction to Tensor Calculus and Continuum
Mechanics, Old Dominion University , 1996.
[19] D. A. Danielson, Vectors and Tensors in Engineering and Physics,
Second Edition , Westview Press, USA, 2003.
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[1] H. Kopka and P. W. Daly, A Guide to LATEX, 3rd ed. Harlow, England:
Addison-Wesley, 1999.
[2] P.A.M. Dirac, General Theory of Relativity, second edition, Princeton
University Press, 1996.
[3] K. Murawski, Analytical and Numerical Methods for wave propagation
in fluid media, World Scientific Publishing Co. Pte. Ltd., Vol. 7, series
A, 2002.
[4] Geroch and Robert, General Relativity from A to B, University of Chicago
Press, Chicago, 1981.
[5] Harish Parthasarathy, Advanced Engineering Physics, First Edition , Ane
books, India, 2006.
[6] A. Vaish and H. Parthasarathy, Finite Element Analysis of Propagation
Modes in a Waveguide: Effect of Gravitational Field, Accepted for
publication in HAIT journal of Engineering and Science, 2007.
[7] D. F. Lawden, An Introduction to Tensor Calculus, Relativity and Cosmology,
Third Edition , Chapman and Hall Ltd, London, 1986.
[8] Cheng and Ta-Pei , Relativity, Gravitation and Cosmology- a Basic
Introduction, Oxford University Press, 2005.
[9] Hartle and James B, Gravity: an Introduction to Einstein-s General
Relativity, San Francisco: Addison-Wesley, 2003.
[10] Arthur Stanley Eddington, The Internal Constitution of the Stars, Cambridge
University Press, Cambridge , 1988.
[11] Arthur Stanley Eddington (1882-1944), H. C. Plummer Obituary Notices
of Fellows of the Royal Society, Vol. 5, No. 14 (Nov., 1945), pp. 113-125.
[12] http://www.time.com/time/magazine/article/0,9171,741025,00.html
[13] J J O-Connor and E F Robertson, "Biography of Paul Adrien
Maurice Dirac (1902-1984)", http://www-groups.dcs.st-and.ac.uk/ history/
Biographies/Dirac.html October 2003.
[14] S.W. Hawking " Encyclopdia Britannica. 2007. Encyclopdia Britannica
Online. 13 Mar. 2007 http://www.britannica.com/eb/article-9039612
[15] L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Fourth
Edition, Published 1987 Elsevier.
[16] L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields,
Pergamon Press, Oxford, 1975.
[17] A. Vaish and H. Parthasarathy, Modal Analysis of Waveguide Using
Finite Element Method, Communicated, 2007.
[18] J. H. Heinbockel, Introduction to Tensor Calculus and Continuum
Mechanics, Old Dominion University , 1996.
[19] D. A. Danielson, Vectors and Tensors in Engineering and Physics,
Second Edition , Westview Press, USA, 2003.
[20] Steven Weinberg, Gravitation and Cosmology- Principles and Applications
of the General Theory of Relativity, First Edition , John Wiley and
sons, 1972.
[21] Hermann Weyl, Space, Time and Matter, Fourth Edition , Dover Publication
Inc., 1952.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54921", author = "Arti Vaish and Harish Parthasarathy", title = "Action Functional of the Electomagnetic Field: Effect of Gravitation", abstract = "The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.
", keywords = "General theory of relativity, electromagnetism, metric tensor, Maxwells equations, test functions, finite element method.", volume = "4", number = "8", pages = "1123-7", }
