TY - JOUR
T1 - A Uniqueness Theorem for the Anti–de Sitter Soliton
AU - Galloway, G. J.
AU - Surya, S.
AU - Woolgar, E.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2002
Y1 - 2002
N2 - 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 anti–de Sitter (AdS) soliton, a globally static, asymptotically toroidal [Formula presented] spacetime with negative mass. Nonetheless, arguing from the AdS conformal field theory (AdS/CFT) correspondence, Horowitz and Myers 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 [Formula presented] 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.
AB - 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 anti–de Sitter (AdS) soliton, a globally static, asymptotically toroidal [Formula presented] spacetime with negative mass. Nonetheless, arguing from the AdS conformal field theory (AdS/CFT) correspondence, Horowitz and Myers 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 [Formula presented] 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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U2 - 10.1103/PhysRevLett.88.101102
DO - 10.1103/PhysRevLett.88.101102
M3 - Article
AN - SCOPUS:85038266465
VL - 88
SP - 4
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 10
ER -