Symmetry analysis and conserved quantities for Lemaitre–Tolman–Bondi spacetimes under f(R) gravity

It is known that the Lemaitre–Tolman–Bondi (LTB) spacetimes describe spherically symmetric radially inhomogeneous models of the universe. Such models have widely been used to study gravitational collapse and late-time cosmic acceleration. In particular, its non-static and inhomogeneous nature can yield ideal models that can be applied in modified gravitational theories. In this paper, we explore non-static LTB spacetimes within the framework of [Formula: see text] gravity, where [Formula: see text] is a function of the scalar curvature [Formula: see text]. To tackle non-linearity of the field equations and to simplify the problem, we restrict the problem to linear model of the [Formula: see text] gravity. In addition to the linear model, we use an algebraic classification of the spacetime components which further help to explore a variety of solutions. In this way, we come across some particular classes of exact LTB solutions to the gravitational field equations in [Formula: see text] gravity. With the help of these solutions, we formulate a geodesic Lagrangian and consequently explore Noether Vector Fields (NVFs). The NVFs link symmetries of the associated Lagrangian to conserved quantities. These conserved quantities may be applied to simplify the dynamical system. For each solution, we compute the corresponding NVFs and note that the dimension of the Noether symmetry algebra for the LTB spacetimes under linear [Formula: see text] gravity is either 7, 9, or 17.