Phase Transitions and Stability of Eguchi-Hanson-AdS Solitons

The Eguchi-Hanson-AdS$_5$ family of spacetimes are a class of static, geodesically complete asymptotically locally AdS$_5$ soliton solutions of the vacuum Einstein equations with negative cosmological constant. They have negative mass and are parameterized by an integer $p\geq 3$ with a conformal boundary with spatial topology $L(p,1)$. We investigate mode solutions of the scalar wave equation on this background and show that, similar to AdS$_5$, the geometry admits a normal mode spectrum (i.e. solutions that neither grow or decay in time). In addition, we also discuss other geometric properties of these soliton spacetimes, including the behaviour of causal geodesics and their thermodynamic properties. We also point out a surprising connection with the AdS soliton.