On certain new exact solutions of the Einstein equations for axisymmetric rotating fields

doi:10.1088/1674-1056/22/10/100203

中国物理B ›› 2013, Vol. 22 ›› Issue (10): 100203-100203.doi: 10.1088/1674-1056/22/10/100203

On certain new exact solutions of the Einstein equations for axisymmetric rotating fields

Lakhveer Kaur, R. K. Gupta

School of Mathematics and Computer Applications, Thapar University, Patiala-147 004, Punjab, India

收稿日期:2013-02-08 修回日期:2013-04-01 出版日期:2013-08-30 发布日期:2013-08-30

On certain new exact solutions of the Einstein equations for axisymmetric rotating fields

Lakhveer Kaur, R. K. Gupta

School of Mathematics and Computer Applications, Thapar University, Patiala-147 004, Punjab, India

Received:2013-02-08 Revised:2013-04-01 Online:2013-08-30 Published:2013-08-30
Contact: Lakhveer Kaur, R. K. Gupta E-mail:lakhveer712@gmail.com;rajeshgupta@thapar.edu

摘要/Abstract

摘要： We investigate the Einstein field equations corresponding to the Weyl-Lewis-Papapetrou form for an axisymmetric rotating field by using the classical symmetry method. Using the invariance group properties of the governing system of partial differential equations (PDEs) and admitting a Lie group of point transformations with commuting infinitesimal generators, we obtain exact solutions to the system of PDEs describing the Einstein field equations. Some appropriate canonical variables are characterized that transform the equations at hand to an equivalent system of ordinary differential equations and some physically important analytic solutions of field equations are constructed. Also, the class of axially symmetric solutions of Einstein field equations including the Papapetrou solution as a particular case has been found.

关键词: Einstein equations, symmetry analysis, exact solutions

Abstract: We investigate the Einstein field equations corresponding to the Weyl–Lewis–Papapetrou form for an axisymmetric rotating field by using the classical symmetry method. Using the invariance group properties of the governing system of partial differential equations (PDEs) and admitting a Lie group of point transformations with commuting infinitesimal generators, we obtain exact solutions to the system of PDEs describing the Einstein field equations. Some appropriate canonical variables are characterized that transform the equations at hand to an equivalent system of ordinary differential equations and some physically important analytic solutions of field equations are constructed. Also, the class of axially symmetric solutions of Einstein field equations including the Papapetrou solution as a particular case has been found.

Key words: Einstein equations, symmetry analysis, exact solutions

中图分类号: (Partial differential equations)

02.30.Jr

02.20.Sv (Lie algebras of Lie groups)

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.

Lakhveer Kaur, R. K. Gupta. On certain new exact solutions of the Einstein equations for axisymmetric rotating fields[J]. Chin. Phys. B, 2013, 22(10): 100203-100203.

参考文献 17

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On certain new exact solutions of the Einstein equations for axisymmetric rotating fields

On certain new exact solutions of the Einstein equations for axisymmetric rotating fields

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