https://doi.org/10.1140/epjc/s10052-018-6164-7
Regular Article - Theoretical Physics
Energy conditions and conservation laws in LTB metric via Noether symmetries
Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan
* e-mail: tahirhussain@uop.edu.pk
Received:
11
June
2018
Accepted:
19
August
2018
Published online:
23
August
2018
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.
Key words: LTB metric / Noether symmetry / Energy conditions / Equation of state
© The Author(s), 2018
