New exact solutions of Einstein–Maxwell equations for magnetostatic fields

doi:10.1088/1674-1056/21/9/090401

中国物理B ›› 2012, Vol. 21 ›› Issue (9): 90401-090401.doi: 10.1088/1674-1056/21/9/090401

New exact solutions of Einstein–Maxwell equations for magnetostatic fields

Nisha Goyal, R. K. Gupta

School of Mathematics and Computer Applications, Thapar University, Patiala-147004, Punjab, India

收稿日期:2011-11-28 修回日期:2012-02-17 出版日期:2012-08-01 发布日期:2012-08-01
基金资助:
Project supported by the Human Resource Development Group Council of Scientific Industrial Research (CSIR), India (Grant No. 09/677(0014)2009-EMR-1).

New exact solutions of Einstein–Maxwell equations for magnetostatic fields

Nisha Goyal, R. K. Gupta

School of Mathematics and Computer Applications, Thapar University, Patiala-147004, Punjab, India

Received:2011-11-28 Revised:2012-02-17 Online:2012-08-01 Published:2012-08-01
Contact: Nisha Goyal E-mail:goyal.n104@gmail.com
Supported by:
Project supported by the Human Resource Development Group Council of Scientific Industrial Research (CSIR), India (Grant No. 09/677(0014)2009-EMR-1).

摘要/Abstract

摘要： The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions.

关键词: Einstein-Maxwell equations, symmetry reduction method, exact solutions

Abstract: The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions.

Key words: Einstein-Maxwell equations, symmetry reduction method, exact solutions

中图分类号: (Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields)

04.40.Nr

02.20.Sv (Lie algebras of Lie groups) 04.20.Jb (Exact solutions)

Nisha Goyal, R. K. Gupta. New exact solutions of Einstein–Maxwell equations for magnetostatic fields[J]. 中国物理B, 2012, 21(9): 90401-090401.

Nisha Goyal, R. K. Gupta. New exact solutions of Einstein–Maxwell equations for magnetostatic fields[J]. Chin. Phys. B, 2012, 21(9): 90401-090401.

参考文献 29

[1]	Lobanov A P 1998 Astron. Astrophys. 79 330
[2]	Aharonian F A 2002 MNRAS 332 215
[3]	Liu Y T, Shapiro S L and Stephens B C 2007 Phys. Rev. D 76 084017
[4]	Vlemmings W H T, Diamond P J and Imai H 2006 Nature 440 58
[5]	Aguilera D N, Pons J A and Miralles J A 2008 Ap. J. 673 L167
[6]	Hennebelle P and Fromang S 2008 Astron. Astrophys. 477 9
[7]	Pavlov G G and Bezchastnov V G 2005 Ap. J. 635 L61
[8]	Ibrahim A I, Swank J H and Parke W 2003 Ap. J. 584 L17
[9]	Reissner H 1916 Ann. Phys. 50 106
[10]	Nordstrom G 1918 Verhandl. Koninkl. Ned. Akad. Wetenschap. Afdel. Natuurk. 26 1201
[11]	Bonnor W B 1953 Proc. Phys. Soc. A 66 145
[12]	Misra M and Radhakrishna L Proc. Nat. Inst. Sci. India A 28 632
[13]	Garcia-Reyes G and Gonjález G A 2007 Brazilian J. Phys. 37 1094
[14]	Stephani H, Kramer D, MacCallum M, Hoenselaers D and Herlt E 2003 Exact Solutions of Einstein Field Equations (2nd edn.) (Cambridge: Cambridge University Press)
[15]	Ji A C, Liu W M, Song J L and Zhou F 2008 Phys. Rev. Lett. 101 010402
[16]	Liang Z X, Zhang Z D and Liu W M 2005 Phys. Rev. Lett. 94 050402
[17]	Liu W M, Wu B and Niu Q 2000 Phys. Rev. Lett. 84 2294
[18]	Singh K and Gupta R K 2006 Int. J. Eng. Sci. 44 1256
[19]	Zhao L, Fu J L and Chen B Y 2010 Chin. Phys. B 19 010301
[20]	Li Y, Fang J H and Zhang K J 2011 Chin. Phys. B 20 030201
[21]	Ma W X and Chen M 2009 Appl. Math. Comp. 215 2835
[22]	Goyal N and Gupta R K 2011 Phys. Scr. 85 015004
[23]	Bhutani O P, Singh K and Kalra D K 2003 Int. J. Eng. Sci. 41 769
[24]	Steinberg S 1979 Symmetry Methods in Differential Equations. Technical Report No. 367 (Albuquerque: University of New Mexico)
[25]	Gandarias M L and Bruzon M S 1998 J. Nonlinear Math. Phys. 5 8
[26]	Attallaha S K, El-Sabbagh M F and Ali A T 2007 Commun. Nonlinear Sci. Numer. Simul. 12 1153
[27]	Ali A T 2009 Phys. Scr. 79 035006
[28]	Bluman G W and Cole J D 1974 Similarity Methods for Differential Equations (New York: Springer-Verlag)
[29]	Ovsiannikov L V 1982 Group Analysis of Differential Equations (New York: Academic Press)

New exact solutions of Einstein–Maxwell equations for magnetostatic fields

New exact solutions of Einstein–Maxwell equations for magnetostatic fields

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 29

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	柴若霖, 谢琼涛, 刘小良. Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials[J]. 中国物理B, 2020, 29(9): 90301-090301.
[2]	杨毅, 蔡绍洪, 隆正文, 陈浩, 龙超云. Exact solution of the (1+2)-dimensional generalized Kemmer oscillator in the cosmic string background with the magnetic field[J]. 中国物理B, 2020, 29(7): 70302-070302.
[3]	董晓菲, 谢幼飞, 陈庆虎. Unified approach to various quantum Rabi models witharbitrary parameters[J]. 中国物理B, 2020, 29(2): 20302-020302.
[4]	Ozkan Guner, Ahmet Bekir. Bright and dark soliton solutions for some nonlinear fractional differential equations[J]. 中国物理B, 2016, 25(3): 30203-030203.
[5]	Hakan Ciftci, H F Kisoglu. Application of asymptotic iteration method to a deformed well problem[J]. 中国物理B, 2016, 25(3): 30201-030201.
[6]	朱维婷, 马松华, 方建平, 马正义, 朱海平. Fusion, fission, and annihilation of complex waves for the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff system[J]. 中国物理B, 2014, 23(6): 60505-060505.
[7]	B. Srividya, L. Kavitha, R. Ravichandran, D. Gopi. Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation[J]. 中国物理B, 2014, 23(1): 10307-010307.
[8]	刘萍, 李子良. Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations[J]. 中国物理B, 2013, 22(5): 50204-050204.
[9]	Vikas Kumar, R. K. Gupta, Ram Jiwari. Comparative study of travelling wave and numerical solutions for the coupled short pulse (CSP) equation[J]. 中国物理B, 2013, 22(5): 50201-050201.
[10]	陈元明, 马松华, 马正义. New exact solutions of (3+1)-dimensional Jimbo-Miwa system[J]. 中国物理B, 2013, 22(5): 50510-050510.
[11]	陈俊超, 李彪, 陈勇. Novel exact solutions of coupled nonlinear Schrödinger equations with time–space modulation[J]. 中国物理B, 2013, 22(11): 110306-110306.
[12]	张聪, 郭文安, 冯世平, 杨师杰. Skyrmion crystals in pseudo-spin-1/2 Bose–Einstein condensates[J]. 中国物理B, 2013, 22(11): 110308-110308.
[13]	Lakhveer Kaur, R. K. Gupta. On certain new exact solutions of the Einstein equations for axisymmetric rotating fields[J]. 中国物理B, 2013, 22(10): 100203-100203.
[14]	杨征, 马松华, 方建平. Soliton excitations and chaotic patterns for the (2+1)-dimensional Boiti–Leon–Pempinelli system[J]. 中国物理B, 2011, 20(6): 60506-060506.
[15]	套格图桑, 那仁满都拉. Constructing infinite sequence exact solutions of nonlinear evolution equations[J]. 中国物理B, 2011, 20(11): 110203-110203.