A uniqueness theorem for the AdS soliton
نویسنده
چکیده
The stability of physical systems depends on the existence of a state of least energy, or ground state. In gravity, this is guaranteed by the positive energy theorem. The proof employs spinor structure and can fail for certain spacetime topologies, such as those arising in non-supersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. The proof also fails for the topology of the adS soliton, a nonsingular Einstein spacetime with negative cosmological constant and negative mass-energy. Nonetheless, arguing from the adS/CFT correspondence, Horowitz and Myers proposed a new positive energy conjecture, stating that the adS soliton is the unique, stable ground state for its asymptotic class. We give a new general structure theorem for negative mass spacetimes and use it to prove uniqueness of the adS soliton. Our work relies on a novel exploitation of the special geometry of ground state spacetimes. It offers significant support for the new positive energy conjecture and adds to the body of rigorous results inspired by the adS/CFT correspondence.
منابع مشابه
On the Geometry and Mass of Static, Asymptotically AdS Spacetimes, and the Uniqueness of the AdS Soliton
We prove two theorems, announced in hep-th/0108170, for static spacetimes that solve Einstein’s equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifolds of non-negative Ricci curvature. For spacetimes with Ricci-flat conformal...
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