Gravitational solitons in anti-de sitter spacetimes

Abstract

A gravitational soliton is a geodesically complete, globally stationary (and horizonfree) non-trivial solution of the Einstein equations, with prescribed asymptotic geometry. It is a classic theorem of Lichnerowicz [1] that in the standard four-dimensional Einstein-Maxwell theory, asymptotically at solitons do not exist, and that the only non-trivial electrovacuum solutions must contain black holes. However, in dimensions greater than four, many explicit asymptotically at examples are now known. This thesis is concerned with gravitational solitons that are asymptotic to (locally) anti-de Sitter (AdS) spacetime. AdS is the maximally symmetric solution of the Einstein equations with negative cosmological constant. Asymptotically AdS geometries have attracted a great deal of interest in theoretical physics over the past two decades. In Chapter 2, we construct supersymmetric, asymptotically AdS5 gravitational soliton solutions of �ve-dimensional gauged supergravity. We show that the solitons contain evanescent ergosurfaces and give an argument that these solitons should be nonlinearly unstable. In Chapter 3, we revisit a well-known example of a gravitational soliton in AdS, the Eguchi-Hanson-AdS5 solution, and investigate a number of its geometric and thermodynamic properties. In particular we show that the linear scalar (Klein-Gordon) wave equation admits normal mode solutions, just like pure AdS. In Chapter 4, we then construct supersymmetric gravitational soliton solutions that are are complete, globally stationary, 1=4-BPS and are asymptotically locally AdS5. Finally, in Chapter 5, we discuss some future directions and ongoing research.