On Birkhoff's Theorem in Horava Gravity

We study Birkhoff's theorem, which states the absence of time-dependent, spherically symmetric vacuum solutions in four-dimensional Horava gravity, which has been proposed as a renormalizable quantum gravity without the ghost problem. We prove that the theorem is still valid for the usual type of solutions which admit the general relativity limit in the low energy (IR) region. However, for the unusual type of solutions, it can be violated in high-energy (UV) region, due to the non-linear effects. This implies that the scalar graviton can emerge as the results of non-linear UV effects but is decoupled in IR regime. An important implication of the non-linear, UV scalar graviton in Big Bang cosmology is also discussed.