Soliton Spacetime Research Articles

Fate of chaotic strings in a confining geometry

We study chaotic motion of classical closed strings in the five-dimensional Anti-de Sitter (AdS) soliton spacetime. We first revisit classical chaos using a cohomogeneity-1 string ansatz. We then consider turbulent behaviors of the classical strings when the spatial dependence of the string world-sheet is included. Sensitivity to initial conditions in chaotic systems suggests that the string under chaos tends to stretch in the AdS soliton spacetime in a Lyapunov timescale. In this process, the orbital angular momentum transfers to internal spin due to the turbulence on the string. It follows that the string stays around the tip of the AdS soliton with a jumbled profile. We evaluate the spectra of conserved quantities and discuss their universal power-law scalings in the turbulent behaviors.

The rigid Horowitz-Myers conjecture

The new positive energy conjecture was first formulated by Horowitz and Myers in the late 1990s to probe for a possible extended, nonsupersymmetric AdS/CFT correspondence. We consider a version formulated for complete, asymptotically Poincaré-Einstein Riemannian metrics (M, g) with bounded scalar curvature R ≥ −n(n − 1) and with no (inner) boundary except possibly a finite union of compact, totally geodesic hypersurfaces (horizons). This version then asserts that any such (M, g) must have mass not less than a certain bound which is realized as the mass m0 of a metric g0 induced on a time-symmetric slice of a spacetime called an AdS soliton. This conjecture remains unproved, having so far resisted standard techniques. Little is known other than that the conjecture is true for metrics which are sufficiently small perturbations of g0. We pose another test for the conjecture. We assume its validity and attempt to prove as a corollary the corresponding scalar curvature rigidity statement, which is that g0 is the unique asymptotically Poincaré-Einstein metric with mass m0 obeying R ≥ −n(n − 1). Were a second such metric g1 not isometric to g0 to exist, it then may well admit perturbations of lower mass, contradicting the assumed validity of the conjecture. We find enough rigidity to show that the minimum mass metric must be static Einstein, so the problem is reduced to that of static uniqueness. When n = 3 the manifold must be isometric to a time-symmetric slice of an AdS soliton spacetime, or must have a non-compact horizon. En route we study the mass aspect, obtaining and generalizing known results: (i) we relate the mass aspect of static metrics to the holographic energy density, (ii) we obtain the conformal invariance of the mass aspect when the bulk dimension is odd, and (iii) we show the vanishing of the mass aspect for negative Einstein manifolds with Einstein conformal boundary.

Holographic entanglement entropy in insulator/superconductor transitions with dark matter sector

We generalize the Stückelberg holographic superconductor model by including dark matter sector in the five-dimensional AdS soliton space–time beyond the probe limit. We study phase transitions with large charge of the scalar field through the condensation of the scalar operator and the holographic topological entanglement entropy of the system. We find that the entanglement entropy is a good probe of the order of phase transitions and second-order critical phase transition points. By investigating the behaviors of the entanglement entropy, we show that the larger coupling parameter [Formula: see text] makes the first-order phase transition more difficult to happen. In all, we conclude that the entanglement entropy can be used to study the effects of the dark matter sector in this general insulator/superconductor system.

Holographic entanglement entropy in insulator/superconductor transition with Born-Infeld electrodynamics

We investigate the holographic entanglement entropy in the insulator/superconductor phase transition for the Born-Infeld electrodynamics with full backreaction in five-dimensional AdS soliton spacetime. We note that the holographic entanglement entropy is a good probe to study the properties of the phase transition, and the Born-Infeld factor $b$ has no effect on the critical chemical potential $\mu_c$. We find that both in the half space and the belt one, the non-monotonic behavior of the entanglement entropy versus the chemical potential is a general property, and the entanglement entropy increases with the increase of the Born-Infeld factor in the superconductor phase. Particularly, there exists confinement/deconfinement phase transition in the strip geometry and the critical width $\ell_c$ is dependent of the Born-Infeld parameter.

The holographic superconductors in higher-dimensional AdS soliton

We explore the behavior of the holographic superconductors at zero temperature for a charged scalar field coupled to a Maxwell field in higher-dimensional AdS soliton spacetime via analytical way. In the probe limit, we obtain the critical chemical potentials increase linearly as a total dimension d grows up. We find that the critical exponent for condensation operator is obtained as 1/2 independently of d, and the charge density is linearly related to the chemical potential near the critical point. Furthermore, we consider a slightly generalized setup the Einstein–Power–Maxwell field theory, and find that the critical exponent for condensation operator is given as 1/(4−2n) in terms of a power parameter n of the Power–Maxwell field, and the charge density is proportional to the chemical potential to the power of 1/(2−n).

Magnetic field effect on the phase transition in AdS soliton spacetime

We investigate the scalar perturbations in an AdS soliton background coupled to a Maxwell field via marginally stable modes. In the probe limit, we study the magnetic field effect on the holographic insulator/superconductor phase transition numerically and analytically. The condensate will be localized in a finite circular region for any finite constant magnetic field. Near the critical point, we find that there exists a simple relation among the critical chemical potential, magnetic field, the charge and mass of the scalar field. This relation indicates that the presence of the magnetic field causes the phase transition hard.

Phase transitions in AdS soliton spacetime through marginally stable modes

We investigate the marginally stable modes of the scalar (vector) perturbations in the AdS soliton background coupled to electric field. In the probe limit, we find that the marginally stable modes can reveal the onset of the phase transitions of this model. The critical chemical potentials obtained from this approach are in good agreement with the previous numerical or analytical results.

Stability of the AdS Soliton Spacetime

Stability of the AdS Soliton Spacetime Gungwon Kang Korea Institute of Science and Technology Information, Daejeon 305-806 Changheon Ohy and Chul H. Leez Department of Physics and BK21 Division of Advanced Research and Education in Physics, Hanyang University, Seoul 133-791 (Received 21 August 2007) The AdS soliton spacetime is a vacuum static solution of ve-dimensional Einstein equations with a cosmological constant. It is asymptotically AdS and regular everywhere without having any curvature singularity or an event horizon inside. Recently, Horowitz and Myers conjectured that this spacetime is the ground state among all spacetime solutions that are asymptotically AdS. If such a conjecture is valid, the spacetime should be stable under small perturbations. We have investigated this issue by numerically studying the full nonlinear evolution of a certain class of perturbations. Our results show that some metric components decay out whereas one metric component grows, indicating a sort of instability. Motivated by this result, we also performed a linearized stability analysis for small perturbations in the same class. Interestingly, our result in such a linearized analysis does not show any indication of instability. Finally, we discuss the implications of our results on the stability of the AdS soliton background. PACS numbers: 04.25.Dm, 04.25.Nx, 04.65.+e

Phase transition of electrically charged Ricci-flat black holes

We study phase transition between electrically charged Ricci-flat black holes and AdS soliton spacetime of Horowitz and Myers in five dimensions. Boundary topology for both of them is S1 × S1 × R2. We consider AdS-Reissner-Nordström black hole and R-charged black holes and find that phase transition of these black holes to AdS soliton spacetime depends on the relative size of two boundary circles. We also perform the stability analysis for these black holes. In order to use the AdS/CFT correspondence, we work in the grand canonical ensemble.

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 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 Chru\'sciel and Simon. We prove equivalence of this mass definition with those of Ashtekar-Magnon and Hawking-Horowitz.