Phase Transitions for Flat Anti–de Sitter Black Holes

Surya, Sumati; Schleich, Kristin; Witt, Donald

doi:10.1103/physrevlett.86.5231

Cited by 112 publications

(164 citation statements)

References 21 publications

(23 reference statements)

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“…This phase transition was interpreted as a confinement/deconfinement transition in the associated large N gauge theory on the boundary [40]. Taking a cue from this, it was shown that a phase transition also occurs between the toroidal black hole and the AdS soliton, and can also be interpreted as a confinement/deconfinement transition in the boundary field theory, in much the same way [37]. Indeed the choice of ground state is crucial to see such a phase transition.…”

Section: Introductionmentioning

confidence: 99%

“…The validity of this conjecture is thus an important test of the nonsupersymmetric version of the AdS/CFT correspondence. 4 A preliminary indication that the soliton is the appropriate ground state comes from a semi-classical thermodynamic analysis of Ricci flat black holes in the background of the AdS soliton [37]. An examination of the thermodynamics of the spherical AdS black hole showed that there is a phase transition that takes place between the black hole and the appropriate ground state, namely AdS spacetime [22].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Geometry and Mass of Static, Asymptotically AdS Spacetimes, and the Uniqueness of the AdS Soliton

Galloway

Surya

Woolgar

2003

Commun. Math. Phys.

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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 boundary, the convexity condition is associated with negative mass. The second theorem is a uniqueness theorem for the negative mass AdS soliton spacetime. This result lends support to the new positive mass conjecture due to Horowitz and Myers which states that the unique lowest mass solution which asymptotes to the AdS soliton is the soliton itself. This conjecture was motivated by a nonsupersymmetric version of the AdS/CFT correspondence. Our results add to the growing body of rigorous mathematical results inspired by the AdS/CFT correspondence conjecture. Our techniques exploit a special geometric feature which the universal cover of the soliton spacetime shares with familiar "ground state" spacetimes such as Minkowski spacetime, namely, the presence of a null line, or complete achronal null geodesic, and the totally geodesic null hypersurface that it determines. En route, we provide an analysis of the boundary data at conformal infinity for the Lorentzian signature static Einstein equations, in the spirit of the Fefferman-Graham analysis for the Riemannian signature case. This leads us to generalize to arbitrary dimension a mass definition for static asymptotically AdS spacetimes given by Chruściel and Simon. We prove equivalence of this mass definition with those of Ashtekar-Magnon and Hawking-Horowitz. *

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Geometry and Mass of Static, Asymptotically AdS Spacetimes, and the Uniqueness of the AdS Soliton

Galloway

Surya

Woolgar

2003

Commun. Math. Phys.

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“…Thus the structure at infinity for the AdS instanton is precisely a compact, flat, ndimensional manifold. The very fact that the instanton is a well-behaved, unique ground state [74][75] [76] for these black holes strongly suggests that vanishing scalar curvature on the boundary is compatible with a stable field theory there, dual to one of these physically well-defined bulk configurations. Thus, we do have a large class of examples in which zero scalar curvature at the boundary is not pathological.…”

Section: Flatness Holography and Seiberg-witten Instabilitymentioning

confidence: 99%

Inflation, large branes, and the shape of space

McInnes

2005

Nuclear Physics B

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Linde has recently argued that compact flat or negatively curved spatial sections should, in many circumstances, be considered typical in Inflationary cosmologies. We suggest that the "large brane instability" of Seiberg and Witten eliminates the negative candidates in the context of string theory. That leaves the flat, compact, three-dimensional manifolds -Conway's platycosms. We show that deep theorems of Schoen, Yau, Gromov and Lawson imply that, even in this case, Seiberg-Witten instability can be avoided only with difficulty. Using a specific cosmological model of the Maldacena-Maoz type, we explain how to do this, and we also show how the list of platycosmic candidates can be reduced to three. This leads to an extension of the basic idea: the conformal compactification of the entire Euclidean spacetime also has the topology of a flat, compact, four-dimensional space.

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“…(45) seems to tell that there is no phase transition when k = 0 or k = −2, which is not always true. There is an argument that it is easier to subtract the action of AdS soliton [24] instead of the vacuum AdS [25]. In this case, besides the temperature, the area of the horizon becomes an independent parameter on which the thermodynamical quantities depend.…”

Section: C-function From Ads Black Hole: No Deformationmentioning

confidence: 99%

One-loop vacuum energy and RG flow induced by double-trace operators in AdS/CFT and dS/CFT correspondence

Nojiri

Odintsov

2004

Phys. Rev. D

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It has been shown that the renormalization group (RG) flow connecting different vacua may occur due to the multi-trace operators in fourdimensional CFT. In the AdS/CFT set-up, the double trace operators correspond to the tachyonic scalar field living in the bulk five-dimensional AdS. In this paper, we consider the five dimensional black hole as the bulk spacetime instead of the pure AdS. In frames of the AdS/CFT correspondence, the AdS black hole is believed to describe dual CFT at finite temperature. From the AdS side, we consider the difference of energies between the two vacua by one-loop calculation for the scalar field with tachyonic mass in five-dimensional AdS black hole. In order to check the dS/CFT correspondence, the corresponding calculations are done in five-dimensional deSitter space. The difference between the two vacua is specified by the difference of the boundary conditions of the scalar field. We show that for AdS black hole, there might occur instability which could be the manifestation of the Hawking-Page phase transition. For stable phase of AdS black hole as well as for deSitter bulk, proposed c-function found beyond the leading order approximation shows the monotonic behaviour consistent with c-theorem.

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Phase Transitions for Flat Anti–de Sitter Black Holes

Cited by 112 publications

References 21 publications

On the Geometry and Mass of Static, Asymptotically AdS Spacetimes, and the Uniqueness of the AdS Soliton

On the Geometry and Mass of Static, Asymptotically AdS Spacetimes, and the Uniqueness of the AdS Soliton

Inflation, large branes, and the shape of space

One-loop vacuum energy and RG flow induced by double-trace operators in AdS/CFT and dS/CFT correspondence

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