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

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

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.

Keywords: Einstein equations symmetry analysis exact solutions

Received: 08 February 2013
Revised: 01 April 2013
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.20.Sv	(Lie algebras of Lie groups)
	04.20.Jb.

Corresponding Authors: Lakhveer Kaur, R. K. Gupta
E-mail: lakhveer712@gmail.com;rajeshgupta@thapar.edu

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Lakhveer Kaur, R. K. Gupta On certain new exact solutions of the Einstein equations for axisymmetric rotating fields 2013 Chin. Phys. B 22 100203

[1]	Stephani H, Kramer D, Maccallum M, Hoenselaers C and Herlt E 2003 Exact Solutions of Einstein’s Field Equations (Cambridge: Cambridge University Press)
[2]	Bluman G W and Kumei S 1989 Symmetries and Differential Equations, Applied Mathematical Sciences (New York: Springer-Verlag)
[3]	Ibragimov N H 1994 CRC Handbook of Lie Group Analysis of Differential Equations: Symmetries, Exact Solutions and Conservation Laws (Florida: CRC Press)
[4]	Ovsiannikov L V 1992 Group Analysis of Differential Equations (New York: Academic Press)
[5]	Olver P J 1993 Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics (Berlin: Springer-Verlag)
[6]	Zhang J F 1995 Acta Phys. Sin. (Overseas Ed., i.e. Chin. Phys.) 4 401
[7]	Msomi A M, Govinder K S and Maharaj S D 2010 J. Phys. A: Math. Theor. 43 285203
[8]	Zhang H Q, Fan E G and Li G 1998 Acta Phys. Sin. (Overseas Ed., i.e. Chin. Phys.) 7 649
[9]	Ruan H Y and Chen Y X 1999 Acta Phys. Sin. (Overseas Ed., i.e. Chin. Phys.) 8 241
[10]	Yao R X, Li Z B and Qu C Z 2004 Chin. Phys. Lett. 21 2077
[11]	Liu H, Li J and Zhang Q 2009 J. Comput. Appl. Math. 228 1
[12]	Johnpillai A G, Khalique C M and Biswas A 2010 Appl. Math. Comput. 216 3114
[13]	Moussa M H M and El-Sheikh R M 2010 Commun. Theor. Phys. 54 603
[14]	Singh K, Gupta R K and Kumar S 2011 Appl. Math. Comput. 217 7021
[15]	Gupta R K and Singh K 2011 Commun. Nonlinear Sci. Numer. Simul. 16 4189
[16]	Wang X Z, Fu H and Fu J L 2012 Chin. Phys. B 21 040201
[17]	Islam J N 1985 Rotating Fields in General Relativity (Cambridge: Cambridge University Press)

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