Symmetry analysis of the Klein-Gordon equation in Bianchi I spacetimes

Abstract

In this work we perform the symmetry classification of the Klein Gordon equation in Bianchi I spacetime. We apply a geometric method which relates the Lie symmetries of the Klein Gordon equation with the conformal algebra of the underlying geometry. Furthermore, we prove that the Lie symmetries which follow from the conformal algebra are also and Noether symmetries for the Klein Gordon equation. We use these resutls in order to determine all the potentials in which the Klein Gordon admits Lie and Noether symmetries. Due to the large number of cases and for easy reference the results are presented in the form of tables. For some of the potentials we use the Lie admitted symmetries to determine the corresponding invariant solution of the Klein Gordon equation. Finally, we show that the results also solve the problem of classification of Lie/Noether point symmetries of the wave equation in Bianchi I spacetime and can be used for the determination of invariant solutions of the wave equation.

accepted for publication by Int. J. Geom. Methods Mod. Phys.; 20 pages, 7 tables

References in corpus (11)

• New results on group classification of nonlinear diffusion-convection equations
• Lie - point and variational symmetries in minisuperspace Einstein's gravity
• Group classification of heat conductivity equations with a nonlinear source
• Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
• Two dimensional dynamical systems which admit Lie and Noether symmetries
• The geometric origin of Lie point symmetries of the Schrödinger and the Klein Gordon equations
• Lie point symmetries of a general class of PDEs: The heat equation
• Symmetries of geodesic motion in Gödel-type spacetimes
• Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations
• Symmetries of Bianchi I space-times
• Autonomous three dimensional Newtonian systems which admit Lie and Noether point symmetries

Cited by in corpus (16)

• One-dimensional optimal system for 2D Rotating Ideal Gas
• Group invariant transformations for the Klein-Gordon equation in three dimensional flat spaces
• Variational Contact Symmetries of Constraint Lagrangians
• Averaging Generalized Scalar Field Cosmologies II: Locally Rotationally Symmetric Bianchi I and flat Friedmann-Lemaître-Robertson-Walker models
• Lie and Noether point Symmetries for a Class of Nonautonomous Dynamical Systems
• Classification of the Lie and Noether point symmetries for the Wave and the Klein-Gordon equations in pp-wave spacetimes
• Shallow-water equations with complete Coriolis force: Group Properties and Similarity Solutions
• Exact solution of the Einstein-Skyrme model in a Kantowski-Sachs spacetime
• Lie symmetries for systems of evolution equations
• Noether Symmetry Analysis of the Klein--Gordon and Wave Equations in Bianchi I Spacetime
• Physical Significance of Noether Symmetries
• Closed-form solutions of the Wheeler-DeWitt equation in a scalar-vector field cosmological model by Lie symmetries
• Linearization of Newton's second law
• Similarity Solutions For The Complex Burgers' Hierarchy
• Bicharacteristics and Fourier integral operators in Kasner spacetime
• Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations