The Instability of Vacua in Gauss-Bonnet Gravity

Abstract

Owing to the quadratic nature of the theory, Einstein-Gauss-Bonnet gravity generically permits two distinct vacuum solutions. One solution (the "Einstein" vacuum) has a well defined limit as the Gauss-Bonnet coupling goes to zero, whereas the other solution (the "stringy" vacuum) does not. There has been some debate regarding the stability of these vacua, most recently from Deser and Tekin who have argued that the corresponding black hole solutions have positive mass and as such both vacua are stable. Whilst the statement about the mass is correct, we argue that the stringy vacuum is still perturbatively unstable. Simply put, the stringy vacuum suffers from a ghost-like instability that is not excited by the spherically symmetric black hole, but would be excited by any source likely to emit gravitational waves, such as a binary system. This result is reliable except in the strongly coupled regime close to the Chern-Simons limit, when the two vacua are almost degenerate. In this regime, we study instanton transitions between branches via bubble nucleation, and calculate the nucleation probability. This demonstrates that there is large mixing between the vacua, so that neither of them can accurately describe the true quantum vacuum. We also present a new gravitational instanton describing black hole pair production in de Sitter space on the Einstein branch, which is preferred to the usual Nariai instantons, and is not present in pure Einstein gravity.