Adil Jhangeer

Conserved Quantities in f(R) Gravity via Noether Symmetry

We investigate f(R) gravity using the Noether symmetry approach. For this purpose, we consider Friedmann Robertson-Walker (FRW) universe and spherically symmetric spacetimes. The Noether symmetry generators are evaluated for some specific choice of f(R) models in the presence of the gauge term. Further, we calculate the corresponding conserved quantities in each case. Moreover, the importance and stability criteria of these models are discussed.

Classification of Cosmic Scale Factor via Noether Gauge Symmetries

In this paper, a complete classification of Friedmann-Robertson-Walker (FRW) spacetime by using approximate Noether approach is presented. Considered spacetime is discussed for three different types of universe i.e. flat, open and closed. Different forms of cosmic scale factor a with respect to the nature of the universe, which posses the nontrivial Noether gauge symmetries (NGS) are reported. The perturbed Lagrangian corresponding to FRW metric in the Noether equation is used to get Noether operators. For different types of universe minimal and maximal set of Noether operators are reported. A list of Noether operators is also computed which is not only independent from the choice of the cosmic scale factor but also from the type of universe. Further, corresponding energy type first integral of motions are also calculated.

Killing and Noether Symmetries of Plane Symmetric Spacetime

This paper is devoted to investigate the Killing and Noether symmetries of static plane symmetric spacetime. For this purpose, five different cases have been discussed. The Killing and Noether symmetries of Minkowski spacetime in cartesian coordinates are calculated as a special case and it is found that Lie algebra of the Lagrangian is 10 and 17 dimensional respectively. The symmetries of Taub’s universe, anti-deSitter universe, self similar solutions of infinite kind for parallel perfect fluid case and self similar solutions of infinite kind for parallel dust case are also explored. In all the cases, the Noether generators are calculated in the presence of gauge term. All these examples justify the conjecture that Killing symmetries form a subalgebra of Noether symmetries (Bokhari et al. in Int. J. Theor. Phys. 45:1063, 2006).

Analytic solutions and conserved quantities of wave equation on torus

This paper discusses the wave equation on torus in terms of classical Lie theory. The symmetry algebra is computed and found solvable. A general element of one-dimensional Lie algebra is used to compute similarity variables. Further invariant solutions are obtained for the considered equation by using similarity variables, while two- and three-dimensional algebras are reported for which the considered equation is investigated by quadrature. Conserved quantities for the considered equation are obtained. The components of conserved vectors are then associated with the translational symmetry generators using the symmetry conservation laws relation given by Kara and Mahomed (2000) [12].

Classification of static plane symmetric spacetime via Noether gauge symmetries

In this paper, general static plane symmetric spacetime is classified with respect to Noether operators. For this purpose, Noether theorem is used which yields a set of linear partial differential equations (PDEs) with unknown radial functions A(r), B(r) and F(r). Further, these PDEs are solved by taking different possibilities of radial functions. In the first case, all radial functions are considered same, while two functions are taken proportional to each other in second case, which further discussed by taking four different relationships between A(r), B(r) and F(r). For all cases, different forms of unknown functions of radial factor r are reported for nontrivial Noether operators with non-zero gauge term. At the end, a list of conserved quantities for each Noether operator Tables 1–4 is presented.

CONSERVATION LAWS FOR THE (1 + 2)-DIMENSIONAL WAVE EQUATION IN BIOLOGICAL ENVIRONMENT

Abstract The derivation of conservation laws for the wave equation on sphere, cone and flat space is considered. The partial Noether approach is applied for wave equation on curved surfaces in terms of the coefficients of the first fundamental form (FFF) and the partial Noether operators determining equations are derived. These determining equations are then used to construct the partial Noether operators and conserved vectors for the wave equation on different surfaces. The conserved vectors for the wave equation on the sphere, cone and flat space are simplified using the Lie point symmetry generators of the equation and conserved vectors with the help of the symmetry conservation laws relation.

Symmetries and generalized higher order conserved vectors of the wave equation on Bianchi I spacetime

Conservation laws of various systems have been studied for decades due to their unparalleled importance in unraveling systems’ intricacies without having to go into microscopic details of the physi...

Noether Gauge Symmetries for Petrov Type D-Levi-Civita Space-Time in Spherical and Cylindrical Coordinates

Petrov Type D-Levi-Civita (DLC) space-time is considered in two different coordinates, that is, spherical and cylindrical. Noether gauge symmetries and their corresponding conserved quantities for respective metric with the restricted range of parameters and coordinates are discussed.