Positive Energy Condition and Conservation Laws in Kantowski-Sachs Spacetime via Noether Symmetries

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.

Projective Collineations of Decomposable Spacetimes Generated by the Lie Point Symmetries of Geodesic Equations

“…The theory of symmetries for differential equations is important for the study of the integrability properties and the determination of conservation laws. The latter can be used to understand the trajectories of geometrical objects such as the orbits of astrophysical objects [62,63]. Furthermore, the procedure for the derivation of the Lie symmetries is straightforward, but is usually a high dimension system and symbolic computation software is usually applied [64].…”

Projective collineations of decomposable spacetimes generated by the Lie point symmetries of geodesic equations

“…The theory of symmetries for differential equations is important for the study of the integrability properties and the determination of conservation laws. The later can be used to understand the trajectories of geometrical objects such are the orbits of astrophysical objects [62,63].…”