A uniqueness theorem for the adS soliton

Details A uniqueness theorem for the adS soliton A uniqueness theorem for the adS soliton

2001-08-22

arxiv.org/abs/hep-th/0108170v2

Phys.Rev.Lett. 88 (2002) 101102

Physics

High Energy Physics

High Energy Physics - Theory

Revtex, 4 pages; Matches published version. More detail in Abstract and one equation corrected. For details of proofs and furt

Scientific paper

10.1103/PhysRevLett.88.101102

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.

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