Energy conditions and conservation laws in LTB metric via Noether symmetries

Abstract

In this paper, we have investigated Noether symmetries in Lemaitre-Tolman-Bondi (LTB) metric. Using the Lagrangian associated with the LTB metric, the set of determining equations for Noether symmetries is obtained and then integrated in several cases. It is shown that the LTB metric can be classified in to eight distinct classes corresponding to Noether algebra of dimension 4, 5, 6, 7, 8, 9, 11 and 17. The obtained Noether symmetries are compared with Killing and homothetic vectors. The well known Noether's theorem is used to find the expressions for conservation laws in each case. Moreover, it is shown that most of the obtained metrics are anisotropic or perfect fluid models which satisfy certain energy conditions and the equation of state.

Energy Conditions and Conservation Laws in LRS Bianchi Type I Spacetimes via Noether Symmetries

“…Conversely, if the vector field X + 2ψs∂ s is an NS, then X is an HV provided that X does not depend on s. [11] In literature, NS, their relation will Killing and homothetic vectors and the corresponding conservation laws have been studied by many researchers, for details we refer to Refs. [11][12][13][14][15][16][17][18][19].…”