Symmetry analysis and conservation laws of the geodesic equations for the Reissner-Nordström de Sitter black hole with a global monopole Mehdi Nadjafikhah, Fatemeh Ahangari ⇑ School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 1684613114, Iran article info Article history: Received 18 August 2011 Received in revised form 14 October 2011 Accepted 20 October 2011 Available online 3 November 2011 Keywords: Reissner-Nordström de Sitter (RNdS) black hole with a global monopole Lie symmetries Optimal system Noether symmetries Conservation laws abstract This paper is devoted to the comprehensive analysis of the problem of symmetries and conservation laws for the geodesic equations of the Reissner-Nordström de Sitter (RNdS) black hole with a global monopole. For this purpose, the system of geodesic equations is determined and the corresponding classical Lie point symmetry operators are obtained. An optimal system of one dimensional subalgebras is constructed and a brief discussion about the algebraic structure of the Lie algebra of symmetries is presented. Also, the Noe- ther symmetries of the geodesic Lagrangian is calculated. Finally, by applying two methods including Noether’s theorem and direct method the conservation laws associated to the system of geodesic equations are obtained. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction As it is well known, phase transitions in the early universe can give rise to topological defects of various kinds such as global monopole, cosmic string, domain wall, texture and so on [17,26]. An approximate solution of Einstein equations for the space–time outside a global monopole was obtained by Barriola and Vilenkin in [3]. By analogue with this metric, Gao and Shen [11] obtained a solution of the Einstein equation which can be described as an electric charged black hole with a monopole in the background of de Sitter space–time. It can be shown that the metric ds 2 ¼Adt 02 þ A 1 dr 02 þ r 02 dh 2 þ sin 2 hdu 2   ; ð1:1Þ A ¼ 1  8pg 2  2M 0 r 0 þ Q 0 2 r 02  1 3 kr 02  ! ; satisfies the Einstein equation [11]. By analogue with the Schwarzschild black hole with a global monopole [3] ds 2 ¼ 1  8pg 2  2M 0 r 0   dt 02 þ 1  8pg 2  2M 0 r 0   1 dr 02 þ r 02 dX 2 2 ; ð1:2Þ 1007-5704/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2011.10.019 ⇑ Corresponding author. Tel.: +98 21 73913426; fax: +98 21 77240472. E-mail addresses: m_nadjafikhah@iust.ac.ir (M. Nadjafikhah), fa_ahangari@iust.ac.ir (F. Ahangari). Commun Nonlinear Sci Numer Simulat 17 (2012) 2350–2361 Contents lists available at SciVerse ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns