A uniqueness theorem for the adS soliton

TL;DR

This paper proves that the AdS soliton is the unique lowest-energy static spacetime with negative cosmological constant, supporting a key conjecture in the context of the AdS/CFT correspondence.

Contribution

It introduces a new structure theorem for static negative cosmological constant spacetimes and proves the uniqueness of the AdS soliton as the minimal energy state.

Findings

Proves the AdS soliton's uniqueness as the lowest-energy static spacetime.

Supports the positive energy conjecture for the AdS soliton.

Enhances understanding of stability in asymptotically AdS spacetimes.

Abstract

The stability of physical systems depends on the existence of a state of least energy. In gravity, this is guaranteed by the positive energy theorem. For topological reasons this fails for nonsupersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. For related reasons, this also fails for the AdS soliton, a globally static, asymptotically toroidal $\Lambda<0$ spacetime with negative mass. Nonetheless, arguing from the AdS/CFT correspondence, Horowitz and Myers (hep-th/9808079) proposed a new positive energy conjecture, which asserts that the AdS soliton is the unique state of least energy in its asymptotic class. We give a new structure theorem for static $\Lambda<0$ spacetimes and use it to prove uniqueness of the AdS soliton. Our results offer significant support for the new positive energy conjecture and add to the body of rigorous results inspired by the AdS/CFT correspondence.