{"title":"Action Functional of the Electomagnetic Field: Effect of Gravitation","authors":"Arti Vaish, Harish Parthasarathy","volume":44,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":1220,"pagesEnd":1227,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/5828","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.<\/p>\r\n","references":"[1] H. Kopka and P. W. Daly, A Guide to LATEX, 3rd ed. Harlow, England:\r\nAddison-Wesley, 1999.\r\n[2] P.A.M. Dirac, General Theory of Relativity, second edition, Princeton\r\nUniversity Press, 1996.\r\n[3] K. Murawski, Analytical and Numerical Methods for wave propagation\r\nin fluid media, World Scientific Publishing Co. Pte. Ltd., Vol. 7, series\r\nA, 2002.\r\n[4] Geroch and Robert, General Relativity from A to B, University of Chicago\r\nPress, Chicago, 1981.\r\n[5] Harish Parthasarathy, Advanced Engineering Physics, First Edition , Ane\r\nbooks, India, 2006.\r\n[6] A. Vaish and H. Parthasarathy, Finite Element Analysis of Propagation\r\nModes in a Waveguide: Effect of Gravitational Field, Accepted for\r\npublication in HAIT journal of Engineering and Science, 2007.\r\n[7] D. F. Lawden, An Introduction to Tensor Calculus, Relativity and Cosmology,\r\nThird Edition , Chapman and Hall Ltd, London, 1986.\r\n[8] Cheng and Ta-Pei , Relativity, Gravitation and Cosmology- a Basic\r\nIntroduction, Oxford University Press, 2005.\r\n[9] Hartle and James B, Gravity: an Introduction to Einstein-s General\r\nRelativity, San Francisco: Addison-Wesley, 2003.\r\n[10] Arthur Stanley Eddington, The Internal Constitution of the Stars, Cambridge\r\nUniversity Press, Cambridge , 1988.\r\n[11] Arthur Stanley Eddington (1882-1944), H. C. Plummer Obituary Notices\r\nof Fellows of the Royal Society, Vol. 5, No. 14 (Nov., 1945), pp. 113-125.\r\n[12] http:\/\/www.time.com\/time\/magazine\/article\/0,9171,741025,00.html\r\n[13] J J O-Connor and E F Robertson, \"Biography of Paul Adrien\r\nMaurice Dirac (1902-1984)\", http:\/\/www-groups.dcs.st-and.ac.uk\/ history\/\r\nBiographies\/Dirac.html October 2003.\r\n[14] S.W. Hawking \" Encyclopdia Britannica. 2007. Encyclopdia Britannica\r\nOnline. 13 Mar. 2007 http:\/\/www.britannica.com\/eb\/article-9039612\r\n[15] L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Fourth\r\nEdition, Published 1987 Elsevier.\r\n[16] L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields,\r\nPergamon Press, Oxford, 1975.\r\n[17] A. Vaish and H. Parthasarathy, Modal Analysis of Waveguide Using\r\nFinite Element Method, Communicated, 2007.\r\n[18] J. H. Heinbockel, Introduction to Tensor Calculus and Continuum\r\nMechanics, Old Dominion University , 1996.\r\n[19] D. A. Danielson, Vectors and Tensors in Engineering and Physics,\r\nSecond Edition , Westview Press, USA, 2003.\r\n[20] Steven Weinberg, Gravitation and Cosmology- Principles and Applications\r\nof the General Theory of Relativity, First Edition , John Wiley and\r\nsons, 1972.\r\n[21] Hermann Weyl, Space, Time and Matter, Fourth Edition , Dover Publication\r\nInc., 1952.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 44, 2010"}