Extra symmetry in the field equations in 5D with spatial spherical symmetry

We point out that the field equations in 5D, with spatial spherical symmetry, possess an extra symmetry that leaves them invariant. This symmetry corresponds to certain simultaneous interchange of coordinates and metric coefficients. As a consequence, a single solution in 5D can generate very different scenarios in 4D, ranging from static configurations to cosmological situations. A new perspective emanates from our work, namely, that different astrophysical and cosmological scenarios in 4D might correspond to the same physics in 5D. We present explicit examples that illustrate this point of view.