Lie symmetries of Lemaitre-Tolman-Bondi metric

The aim of this paper is to investigate Lie symmetries including Killing, homothetic and conformal symmetries of Lemaitre-Tolman-Bondi (LTB) spacetime metric. To find all LTB metrics admitting these three types of symmetries, we have analyzed the set of symmetry equations by a Maple algorithm that provides some restrictions on the functions involved in LTB metric under which this metric admits the three mentioned symmetries. The solution of symmetry equations under these restrictions leads to the explicit form of symmetries. The stress-energy tensor is calculated for all the obtained metrics in order to discuss their physical significance. It is noticed that most of these metrics satisfy certain energy conditions and correspond to anisotropic fluids.