Exact novel class of spherically symmetric solutions and their conformal vector fields in symmetric teleparallel gravity

In this paper, we investigate a static spherically symmetric (SS) space-time and derive several exact solutions of the field equations. The resulting solutions include Constant red-shift, Quadratic potential screening, Logarithmic quadratic potential, Inverse quadratic scaling and Schwarzschild-Ads-type solutions. Motivated by role of conformal symmetry in revealing hidden geometry structure, we determine the conformal vector fields (CVFs) admitted by each solution. We find that dimension of CVFs is either four or six. To the best of our knowledge, this provides the first systematic conformal symmetry of exact static SS solutions in f ( Q ) gravity. Furthermore, we reconstruct f ( Q ) gravity models for each solution, thereby obtaining the explicit functional forms consistent with the derived geometries. Our results provide new exact background solutions together with their conformal symmetry in f ( Q ) gravity.