Abstract
In this paper, we have investigated Noether symmetries of the Lagrangian of Kantowski–Sachs spacetime. The associated Lagrangian of the Kantowski–Sachs metric is used to derive the set of determining equations. Solving the determining equations for several values of the metric functions, it is observed that the Kantowski–Sachs spacetime admits the Noether algebra of dimensions 5, 6, 7, 8, 9, and 11. A comparison of the obtained Noether symmetries with Killing and homothetic vectors is also presented. With the help of Noether’s theorem, we have presented the expressions for conservation laws corresponding to all Noether symmetries. It is observed that the positive energy condition is satisfied for most of the obtained metrics.
Highlights
IntroductionAmong the approaches followed for obtaining the exact solutions of Einstein’s field equations (EFEs), the most popular is to use some symmetry restrictions on the tensor gab
Einstein’s field equations (EFEs), Gab = kTab, are ten-tensor equations, which describe the gravitational effects produced by a given mass in a spacetime
A Lorentz metric gab is regarded as an exact solution of EFEs if it is obtained by solving the EFEs exactly in closed form and is conformable to a physically realistic Tab
Summary
Among the approaches followed for obtaining the exact solutions of EFEs, the most popular is to use some symmetry restrictions on the tensor gab These restrictions are mathematically expressed as L X gab = 0, where X is called a Killing vector (KV) and L denotes the Lie derivative operator. The study of NS is important due to the fact that it usually provides the additional conservation laws, not given by KVs. If the Killing and Noether algebras are denoted by K ( M) and N ( M ), respectively, K ( M ) ⊆ N ( M ). The same authors discussed the existence of lump solutions involving free parameters for some nonlinear partial differential equations that present Lie symmetries and that may generate associated conservation laws [26].
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