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Energy-Momentum Density's Conservation Law Of International Journal of Advanced Research in Physical Science (IJARPS) Volume 6, Issue 7, 2019, PP 27-29 ISSN No. (Online) 2349-7882 www.arcjournals.org Energy-Momentum Density’s Conservation Law of Electromagnetic Field in Rindler Space-time Sangwha-Yi* Department of Math, Taejon University 300-716 *Corresponding Author: Sangwha-Yi, Department of Math, Taejon University 300-716 . Abstract: We find the energy-momentum density of electromagnetic field by energy-momentum tensor of electromagnetic field in Rindler space-time. We find the energy-momentum density’s conservation law of electromagnetic field in Rindler spacetime. Keywords: The general relativity theory, The Rindler spacetime, Energy-momentum density, Conservation law PACS: 04,04.90.+e, 41.20 1. INTRODUCTION Our article’s aim is that we find the energy-momentum density of electromagnetic field by energy- momentum tensor of electromagnetic field in Rindler space-time. We find the energy-momentum density’s conservation law of electromagnetic field in Rindler space-time. In inertial frame, the energy-momentum tensor T of the electromagnetic field is 1 1 T (F F F F ) (1) 4c 4 In this time, in inertial frame, Faraday tensors F ,F are 0 E x E y E z 0 E E E x y z E 0 B B x z y , E 0 B B (2) F F x z y E B 0 B E B 0 B y z x y z x E B B 0 E B B 0 z y x z y x 0 Hence, the energy density p f and the momentum density p f of electromagnetic field are 2 2 0 00 E B 0i E B T p f , T p ,i 1,2,3 8c f 4c E E ,B B (3) In inertial frame, the energy-momentum conservation law of electromagnetic field is by Noether theorem, 00 0i T , T ,0 T ,i , 1 E 2 B 2 E B ( ) ( ) 0 (4) c t 8c 4c 2. ENERGY-MOMENTUM DENSITY'S CONSERVATION ELECTROMAGNETIC FIELD IN RINDLER SPACETIME Rindler space-time is a 1 1 1 d 2 (1 0 )(d 0 )2 [(d 1 )2 (d 2 )2 (d 3 )2 ] g d d (5) c 2 c 2 c 2 In Rindler space-time, the energy-momentum tensor of the electromagnetic field is International Journal of Advanced Research in Physical Science (IJARPS) Page | 27 Energy-Momentum Density’s Conservation Law of Electromagnetic Field in Rindler Space-time 1 1 T (F F g F F ) (6) 4c 4 In this time, in Rindler space-time, Faraday tensor F is[2] 0 E 1 E 2 E 3 1 1 a 0 a 0 E 1 0 (1 )B 3 (1 )B 2 c 2 c 2 (7) F 1 1 a 0 a 0 E 2 (1 )B 3 0 (1 )B 1 c 2 c 2 a 1 a 1 0 0 E 3 (1 )B 2 (1 )B 1 0 c 2 c 2 In Rindler space-time, Faraday tensor F is[2] 1 1 1 a 0 a 0 a 0 0 (1 )E 1 (1 )E 2 (1 )E 3 c 2 c 2 c 2 a 1 (1 0 )E 0 B B (8) 2 1 3 2 F c 1 a 0 (1 )E 2 B 3 0 B 1 c 2 a 1 0 (1 )E 3 B 2 B 1 0 c 2 0 Hence, the energy density p and the momentum density p of electromagnetic field are in Rindler f f space-time. 2 2 0 1 E B T 00 p (9) f a 1 8c (1 0 ) c 2 E B T 0i p , (10) f 4c E E ,B B (11) In Rindler space-time, the energy-momentum conservation law of electromagnetic field is by Noether theorem, 00 0i 0 i 1,2,3 T ; T ;0 T ;i T ; , i 1,2,3 0 T 0 0 T T (12) x In this time, affine connections are in Rindler space-time 1 a 0 1 a 0 00 (1 ) , 0 0 1 a 0 (13) c 2 c 2 10 01 a 1 c 2 (1 0 ) c 2 Hence, in Rindler space-time, the energy-momentum conservation law of electromagnetic field is 0 T 0 01 3 01T x International Journal of Advanced Research in Physical Science (IJARPS) Page | 28 Energy-Momentum Density’s Conservation Law of Electromagnetic Field in Rindler Space-time E 2 B 2 E B 1 1 1 a 0 1 0 ( ) ( ) 3 (E 3 B 2 E 2 B 3 ) a 1 c 0 8c 4c a 1 c 2 4c (1 0 ) (1 0 ) c 2 c 2 ( , , ) 1 2 3 E E ,B B (14) 3. CONCLUSION We find the energy-momentum density’s conservation law of electromagnetic field in Rindler space- time. REFERENCES [1] S.Yi, “Electromagnetic field equation and Lorentz Gauge in Rindler Space-time”,The African Review of Physics,11,33(2016)-INSPIRE-HEP [2] S.Yi, “Einstein’s Notational Equation of Electro-Magnetic Field Equation in Rindler space-time”, International Journal of Advanced Research in Physical Science,6,5(2019)pp 4-6 [3] S.Weinberg,Gravitation and Cosmology(John wiley & Sons,Inc,1972) [4] W.Rindler, Am.J.Phys.34.1174(1966) [5] P.Bergman,Introduction to the Theory of Relativity(Dover Pub. Co.,Inc., New York,1976),Chapter V [6] C.Misner, K,Thorne and J. Wheeler, Gravitation(W.H.Freedman & Co.,1973) [7] S.Hawking and G. Ellis,The Large Scale Structure of Space-Time(Cam-bridge University Press,1973) [8] R.Adler,M.Bazin and M.Schiffer,Introduction to General Relativity(McGraw-Hill,Inc.,1965) [9] A.Miller, Albert Einstein’s Special Theory of Relativity(Addison-Wesley Publishing Co., Inc., 1981) [10] W.Rindler, Special Relativity(2nd ed., Oliver and Boyd, Edinburg,1966) [11] J.W.Maluf and F.F.Faria,”The electromagnetic field in accelerated frames”:Arxiv:gr-qc/1110.5367v1(2011) [12] Massimo Pauri, Michele Vallisner, "Marzke-Wheeler coordinates for accelerated observers in special relativity":Arxiv:gr-qc/0006095(2000) Citation: Sangwha-Yi, (2019). Energy-Momentum Density’s Conservation Law of Electromagnetic Field in Rindler Space-time. International Journal of Advanced Research in Physical Science (IJARPS) 6(7), pp.27- 29, 2019. Copyright: © 2019 Authors, this is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. International Journal of Advanced Research in Physical Science (IJARPS) Page | 29 .
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