Symmetries and Relativity

Call for Papers

Symmetry lies at the heart of the concept of elegance, especially in mathematics and physics. It was explicitly used by Abel and Galois to prove that quintic and higher order algebraic polynomial equations cannot be solved by means of radicals and developed into group theory. Lie developed Lie symmetry analysis to use groups to deal with differential equations. It provides transformation methods to obtain exact solutions of nonlinear differential equations.

In the twentieth century group theory entered into fundamental physics in a major way, with Noether’s theorem, and was used in quantum mechanics, condensed matter physics, what was earlier called “particle physics,” and relativity, where it enters through the use of differential geometry. In particular, relativity essentially needs the exact solution of the Einstein field equations where possible, which are, in general, ten coupled nonlinear partial differential equations for ten functions of four variables. Symmetries are used to reduce the complexity of the problem to solve uncoupled ordinary differential equations. They also provide the conservation laws for those solutions. As such, symmetry is a crucial tool in the armory of relativists. It turns out that geometric methods enhance the capability of solving systems of nonlinear ordinary differential equations. This link makes it natural for relativists to enter into Lie symmetry analysis.

We invite researchers to contribute original research articles or review articles in the areas of Lie symmetry analysis and its applications, particularly in relativity. We are particularly interested in articles that use methods stemming from one area into the other. Potential topics include, but are not limited to:

• Lie symmetries of systems of ordinary differential equations
• Lie symmetries of systems of partial differential equations
• Hidden symmetries
• Bi-Hamiltonian systems
• Linearization of systems of differential equations
• Conservation laws and Noether or partial Noether symmetries
• Complex methods for systems of differential equations
• Symmetries and exact solutions of Einstein’s field equations
• Symmetries of the geometrical quantities occurring in relativity
• Symmetries of the physical quantities occurring in relativity

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/amp/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/submit/journals/amp/symr/ according to the following timetable:

Lead Guest Editor

• Asghar Qadir, Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, H-12, Islamabad, Pakistan

Guest Editors

• Graham Hall, Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3UE, UK
• Fazal M. Mahomed, School for Computational & Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
• Filipe C. Mena, Department of Mathematics and Applications, University of Minho,Braga, Portugal
• Gazanfer Unal, Department of International Finance, Yeditepe University, Istanbul, Turkey