Violation of Birkhoff's theorem for pure quadratic gravity action

We investigate the application of Birkhoff's theorem to Einstein's quadratic conjecture for the vacuum action. A derivation of the vacuum solution follows from the general metric ansatz for an uncharged, spherically symmetric and static stellar object. It is shown that the Schwarzschild-de Sitter metric is not the only static solution for the quadratic field equation in vacuum. Moreover, with a time dependency as starting point in the metric ansatz, we find a time-dependent solution. The existence of such a solution implies that Birkhoff's theorem is not strictly valid for the quadratic gravity Lagrangian.