Exact solutions of Einstein field equations in perfect fluid distribution using Lie symmetry method

Jyoti, Divya; Kumar, Sachin; Gupta, Rajesh Kumar

doi:10.1140/epjp/s13360-020-00622-2

Cited by 10 publications

(4 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Case 2. Analogous to the vector field V 7 + αV 5 , the symmetric variables are: (10) where A, B, D, E, G are new dependent functions and s is new independent variable. On replacing the above variables in (3), the system (3) can be diminished to ODE system as…”

Section: Reduction By Using Symmetries and Exact Solutionsmentioning

confidence: 99%

“…This semi-Riemannian manifold [24] is not conformally flat. The Lie symmetry method [9,10,[16][17][18]30] is used to find the symmetry groups [3,15], performing symmetry reduction and for getting the exact solutions in terms of integrable arbitrary functions. On letting the doubly periodic Jacobi elliptic functions in place of arbitrary functions, the 3D plots and 2D plots are shown.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

General form of axially symmetric stationary metric: exact solutions and conservation laws in vacuum fields

Jyoti¹,

Kumar²

2023

Class. Quantum Grav.

Self Cite

View full text Add to dashboard Cite

The invariant non-static solutions of Einstein’s vacuum field equations, corresponding to the most general form of axially symmetric stationary line element that represents a non conformally flat semi-Riemannian spacetime in cylindrical coordinates, are investigated. Lie symmetry method is used for symmetry reduction as well as for obtaining exact solutions in terms of arbitrary functions. The conservation laws are obtained for vacuum equations in axially symmetric gravitational fields. The solutions of Lewis metric and Chandrasekhar metric, are derived from the obtained solutions. By considering the possibilities of arbitrary functions, the graphical behaviour of the solutions is also shown.

show abstract

Section: Reduction By Using Symmetries and Exact Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

General form of axially symmetric stationary metric: exact solutions and conservation laws in vacuum fields

Jyoti¹,

Kumar²

2023

Class. Quantum Grav.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Lie group method [1,19] is a powerful method to find the invariant solutions of system of nonlinear differential equations. This method is used for finding the symmetries, for symmetry reduction [15] and for finding the invariant solutions of system of nonlinear partial differential equations (PDEs) [11,12,13,14]. By using this method, the invariant solutions of the DGH equation have been found by Gupta and Anupma [9] as well as, the invariant solutions of the dissipative DGH equation have been found by Wei and Wang [24].…”

Section: Copyright C 2022 the Author(s) Published By Vilnius Gedimina...mentioning

confidence: 99%

Generalised Two-Component Modified Weakly Dissipative Dullin-Gottwald-Holm System: Invariance Analysis and Conservation Laws

Kumar

Jyoti

2022

Mathematical Modelling and Analysis

Self Cite

View full text Add to dashboard Cite

The Dullin-Gottwald-Holm equation models the unidirectional propagation of shallow regime water waves. In this work, the Lie symmetry analysis of the generalised two-component modified weakly dissipative Dullin-Gottwald-Holm system is performed. Using symmetry reduction, the exact solutions are obtained in the form of power series and trigonometric functions. Also using multiplier approach, the conservation laws are obtained. The 3D graphical representations are also shown for obtained solutions.

show abstract

“…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. The exact vacuum accelarating non-static solutions have also been derived by Jyoti et al [16] using Lie symmetry approach.…”

Section: Introductionmentioning

confidence: 99%

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

Dalal,

Singh,

Kumar

2024

Commun. Theor. Phys.

Self Cite

View full text Add to dashboard Cite

In this paper, the non-static solutions for perfect fluid distribution with plane symmetry in f(R,T) gravitational theory are obtained. Firstly using the Lie symmetries, symmetry reductions are performed for considered vector fields to reduce the number of independent variables. Then, corresponding to each reduction, exact solutions are obtained. Killing vectors leads to different conserved quantities. There- fore, we figure out the Killing vector fields corresponding to all derived solutions. The derived solutions are further studied and it is observed that all of the obtained spacetimes, atleast admit the min- imal symmetry group consists of ∂y, ∂z and −z∂y + y∂z. The obtained metrics, admit 3, 4, 6, and 10, Killing vector fields. Con- servation of linear momentum in direction of y and z and angu- lar momentum along x axis is provided by all derived solutions.

show abstract

Exact solutions of Einstein field equations in perfect fluid distribution using Lie symmetry method

Cited by 10 publications

References 23 publications

General form of axially symmetric stationary metric: exact solutions and conservation laws in vacuum fields

General form of axially symmetric stationary metric: exact solutions and conservation laws in vacuum fields

Generalised Two-Component Modified Weakly Dissipative Dullin-Gottwald-Holm System: Invariance Analysis and Conservation Laws

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

Contact Info

Product

Resources

About