On Birkhoff's Theorem in Horava Gravity

TL;DR

This paper investigates Birkhoff's theorem within Horava gravity, showing its validity in IR but potential violation in UV due to non-linear effects, with implications for scalar gravitons and cosmology.

Contribution

It proves Birkhoff's theorem holds in IR but can be violated in UV in Horava gravity, highlighting the emergence of scalar gravitons from non-linear UV effects.

Findings

Birkhoff's theorem is valid in IR for Horava gravity.

In UV, non-linear effects can violate Birkhoff's theorem.

Scalar graviton may emerge from UV effects, affecting cosmology.

Abstract

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.