On the geometric properties of AdS instantons

According to the positive energy conjecture of Horowitz and Myers, there is a specific supergravity solution, AdS soliton, which has minimum energy am ong all asymptotically locally AdS solutions with the same boundary conditi ons. Related to the issue of semiclassical stability of AdS soliton in the context of pure gravity with a negative cosmological constant, physical bou ndary conditions are determined for an instanton solution which would be re sponsible for vacuum decay by barrier penetration. Certain geometric proper ties of instantons are studied, using hermitean differential operators. On a d-dimensional instanton, it is shown that there are d - 2 harmonic functi ons. A class of instanton solutions, obeying more restrictive boundary cond itions, is proved to have d - 1 Killing vectors which also commute. All but one of the Killing vectors are duals of harmonic one-forms, which are grad ients of harmonic functions, and do not have any fixed points.