On new symmetries and exact solutions of Einstein’s field equation for perfect fluid distribution

Abstract

Some new infinite-dimensional generalised Lie symmetries of Einstein's field equations for perfect fluid distribution are found by using the Lie symmetry analysis. The reduced ordinary differential equations are solved to obtain new non-trivial exact solutions. The software MAPLE is used for computation and MAPLE code is given to facilitate the research in this field.

Non-static plane symmetric perfect fluid solutions and Killing symmetries in f(R, T) gravity

“…Now we will perform Lie symmetry analysis of differential equation (12). Let us consider one parameter Lie group of transformations [9] for (12)…”

“…Using (13) in equation (12), and then solving the system of corresponding determining equations gives the following infinitesimals…”

“…where P is the new dependent variable of independent variable r. Using these relations in (12), the reduced ordinary differential equation…”

“…However, when it comes to non-linearity of DEs, the Lie symmetry method [9] has been proved most effective. Many authors have derived exact solutions of FEs in GR using this method [10][11][12][13][14]. Jyoti et al [15] has used symmetry analysis in order to find the perfect fluid solutions for Einstein field equations.…”