Kengo Maeda

Fate of the black string instability

Gregory and Laflamme showed that certain nonextremal black strings (and p-branes) are unstable to linearized perturbations. It is widely believed that this instability will cause the black string horizon to classically pinch off and then quantum mechanically separate, resulting in higher dimensional black holes. We argue that this cannot happen. Under very mild assumptions, classical event horizons cannot pinch off. Instead, they settle down to new static black string solutions which are not translationally invariant along the string.

Black holes with scalar hair and asymptotics in N=8 supergravity

We consider = 8 gauged supergravity in D = 4 and D = 5. We show one can weaken the boundary conditions on the metric and on all scalars with m2 < − (D − 1)2/4 + 1 while preserving the asymptotic anti-de Sitter (AdS) symmetries. Each scalar admits a one-parameter family of AdS-invariant boundary conditions for which the metric falls off slower than usual. The generators of the asymptotic symmetries are finite, but generically acquire a contribution from the scalars. For a large class of boundary conditions we numerically find a one-parameter family of black holes with scalar hair. These solutions exist above a certain critical mass and are disconnected from the Schwarschild-AdS black hole, which is a solution for all boundary conditions. We show the Schwarschild-AdS black hole has larger entropy than a hairy black hole of the same mass. The hairy black holes lift to inhomogeneous black brane solutions in ten or eleven dimensions. We briefly discuss how generalized AdS-invariant boundary conditions can be incorporated in the AdS/CFT correspondence.

Vortex lattice for a holographic superconductor

We investigate the vortex lattice solution in a (2+1)-dimensional holographic model of superconductors constructed from a charged scalar condensate. The solution is obtained perturbatively near the second-order phase transition and is a holographic realization of the Abrikosov lattice. Below a critical value of the magnetic field, the solution has a lower free energy than the normal state. Both the free-energy density and the superconducting current are expressed by nonlocal functions, but they reduce to the expressions in the Ginzburg-Landau theory at long wavelengths. As a result, a triangular lattice becomes the most favorable solution thermodynamically, as in the Ginzburg-Landau theory of type II superconductors.

Characteristic length of an AdS/CFT superconductor

We investigate in more detail the holographic model of a superconductor recently found by Hartnoll, Herzog, and Horowitz [Phys. Rev. Lett. 101, 031601 (2008)], which is constructed from a condensate of a charged scalar field in AdS{sub 4}-Schwarzschild background. By analytically studying the perturbation of the gravitational system near the critical temperature T{sub c}, we obtain the superconducting coherence length proportional to 1/{radical}(1-T/T{sub c}) via AdS/CFT (anti-de Sitter/conformal field theory) correspondence. By adding a small external homogeneous magnetic field to the system, we find that a stationary diamagnetic current proportional to the square of the order parameter is induced by the magnetic field. These results agree with Ginzburg-Landau theory and strongly support the idea that a superconductor can be described by a charged scalar field on a black hole via AdS/CFT duality.

Stability and thermodynamics of AdS black holes with scalar hair

Recently a class of static spherical black hole solutions with scalar hair was found in four and five dimensional gauged supergravity with modified, but anti-de Sitter (AdS) invariant boundary conditions. These black holes are fully specified by a single conserved charge, namely, their mass, which acquires a contribution from the scalar field. Here we report on a more detailed study of some of the properties of these solutions. A thermodynamic analysis shows that in the canonical ensemble the standard Schwarzschild-AdS black hole is stable against decay into a hairy black hole. We also study the stability of the hairy black holes and find there always exists an unstable radial fluctuation, in both four and five dimensions. We argue, however, that Schwarzschild-AdS is probably not the end state of evolution under this instability.

Dynamic critical phenomena in the AdS/CFT duality

In critical phenomena, singular behaviors arise not only for thermodynamic quantities but also for transport coefficients. We study this dynamic critical phenomenon in the AdS/CFT duality. We consider black holes with a single R-charge in various dimensions and compute the R-charge diffusion in the linear perturbations. In this case, the black holes belong to model B according to the classification of Hohenberg and Halperin.

Generic Cosmic-Censorship Violation in anti-de Sitter Space

We consider (four-dimensional) gravity coupled to a scalar field with potential V(phi). The potential satisfies the positive energy theorem for solutions that asymptotically tend to a negative local minimum. We show that for a large class of such potentials, there is an open set of smooth initial data that evolve to naked singularities. Hence cosmic censorship does not hold for certain reasonable matter theories in asymptotically anti-de Sitter spacetimes. The asymptotically flat case is more subtle. We suspect that potentials with a local Minkowski minimum may similarly lead to violations of cosmic censorship in asymptotically flat spacetimes, but we do not have definite results.

Inhomogeneous near-extremal black branes

It has recently been shown that there exist stable inhomogeneous neutral black strings in higher dimensional gravity. These solutions were motivated by the fact that the corresponding homogeneous solutions are unstable. We show that there exist new inhomogeneous black string and black p-brane solutions even when the corresponding translationally invariant solutions are stable. In particular, we show there exist inhomogeneous near-extremal black strings and p-branes. Some of these solutions remain inhomogeneous even when the size of the compact direction (at infinity) is very small.

Study of anisotropic black branes in asymptotically anti-de Sitter

A bstractWe investigate the four dimensional gravitational theories which admit homogeneous but anisotropic black brane solutions in asymptotically AdS space-time. The gravitational theories we consider are 1) Einstein-Maxwell-dilaton theory, and 2) EinsteinMaxwell-dilaton-axion theory with SL(2, R) symmetry. We obtain the solutions both analytically and numerically. Analytical solutions are obtained by perturbation from the isotropic solutions. Our solutions approach singular behavior at the horizon in the extremal limit but in non-extremal case, they are smooth everywhere. We also discuss how the third law of thermodynamics holds in our set-up.

Negative energy in string theory and cosmic censorship violation

We find asymptotically anti\char21{}de Sitter solutions in