A Note on Lie Algebra of Killing Vector Fields of Locally Rotationally Symmetric Bianchi Type-I Spacetime in f(Q)-Gravity

The goal of this paper is to derive the Lie algebra of Killing vector fields for the locally rotationally symmetric Bianchi type-I spacetime within the framework of f(Q) gravity, where f(Q) gravity is a modified gravitational theory that extends General Relativity by introducing a function of the non-metricity tensor Q to explore alternative models of gravity. To achieve this, various algebraic methods and direct integration techniques are employed. Different metric functions are analyzed, and the associated Killing vectors are determined for each case. It is observed that the spacetime under investigation can support either4, 6, or 10 Killing vector fields.