Violation of Birkhoff's theorem for pure quadratic gravity action

Abstract

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.