Instability of a two-dimensional extremal black hole

We consider the perturbation of tachyon about the extremal ground state of a two-dimensional (2D) electrically charged black hole. It is found that the presenting potential to on-coming tachyonic wave takes a double-humped barrier well. This allows an exponentially growing mode with respect to time. This extremal ground state is classically unstable. We conclude that the 2D extremal electrically charged black hole cannot be a candidate for the stable endpoint of the Hawking evaporation.Comment: 9 pages 2 figures, RevTeX, to be published in Phys. Rev D, to obtain gifures contact Author ([email protected]

The Fisher-Rao metric for projective transformations of the line

A conditional probability density function is defined for measurements arising from a projective transformation of the line. The conditional density is a member of a parameterised family of densities in which the parameter takes values in the three dimensional manifold of projective transformations of the line. The Fisher information of the family defines on the manifold a Riemannian metric known as the Fisher-Rao metric. The Fisher-Rao metric has an approximation which is accurate if the variance of the measurement errors is small. It is shown that the manifold of parameter values has a finite volume under the approximating metric. These results are the basis of a simple algorithm for detecting those projective transformations of the line which are compatible with a given set of measurements. The algorithm searches a finite list of representative parameter values for those values compatible with the measurements. Experiments with the algorithm suggest that it can detect a projective transformation of the line even when the correspondences between the components of the measurements in the domain and the range of the projective transformation are unknown

Cosmic holographic bounds with UV and IR cutoffs

We introduce the cosmic holographic bounds with two UV and IR cutoff scales, to deal with both the inflationary universe in the past and dark energy in the future. To describe quantum fluctuations of inflation on sub-horizon scales, we use the Bekenstein-Hawking energy bound. However, it is not justified that the D-bound is satisfied with the coarse-grained entropy. The Hubble bounds are introduced for classical fluctuations of inflation on super-horizon scales. It turns out that the Hubble entropy bound is satisfied with the entanglement entropy and the Hubble temperature bound leads to a condition for the slow-roll inflation. In order to describe the dark energy, we introduce the holographic energy density which is the one saturating the Bekenstein-Hawking energy bound for a weakly gravitating system. Here the UV (IR) cutoff is given by the Planck scale (future event horizon), respectively. As a result, we find the close connection between quantum and classical fluctuations of inflation, and dark energy.Comment: 15page

BTZ black hole and quantum Hall effect in the bulk/boundary dynamics

We point out an interesting analogy between the BTZ black hole and QHE (Quantum Hall effect) in the (2+1)-dimensional bulk/boundary theories. It is shown that the Chern-Simons/Liouville(Chern-Simons/chiral boson) is an effective description for the BTZ black hole (QHE). Also the IR(bulk)-UV(boundary) connection for a black hole information bound is realized as the UV(low-lying excitations on bulk)-IR(long-range excitations on boundary) connection in the QHE. An inflow of conformal anomaly($c=1$ central charge) onto the timelike boundary of AdS$_3$ by the Noether current corresponds to an inflow of chiral anomaly onto the edge of disk by the Hall current.Comment: 8 pages, this version to appear in Phys. Rev.

Unitarity issue in BTZ black holes

We study the wave equation for a massive scalar in three-dimensional AdS-black hole spacetimes to understand the unitarity issues in a semiclassical way. Here we introduce four interesting spacetimes: the non-rotating BTZ black hole (NBTZ), pure AdS spacetime (PADS), massless BTZ black hole (MBTZ), and extremal BTZ black hole (EBTZ). Our method is based on the potential analysis and solving the wave equation to find the condition for the frequency $\omega$ exactly. In the NBTZ case, one finds the quasinormal (complex and discrete) modes which signals for a non-unitary evolution. Real and discrete modes are found for the PADS case, which means that it is unitary obviously. On the other hand, we find real and continuous modes for the two extremal black holes of MBTZ and EBTZ. It suggests that these could be candidates for the unitary system.Comment: 14 pages, contracted version to appear in MPL

Nonpropagation of massive mode on AdS2 in topologically massive gravity

Making use of Achucarro-Ortiz (AO) type of dimensional reduction, we study the topologically massive gravity with a negative cosmological constant on AdS2 spacetimes. For a constant dilaton, this two-dimensional model also admits three AdS2 vacuum solutions, which are related to two AdS3 and warped AdS3 backgrounds with an identification upon uplifting three dimensions. We carry out the perturbation analysis around these backgrounds to find what is a physically propagating field. However, it turns out that there is no propagating massive mode on AdS2 background, in contrast to the Kaluza-Klein (KK) type of dimensional reduction. We note that two dimensionally reduced actions are different and thus, the non-equivalence of their on-shell amplitudes is obtained.Comment: 19 pages, version to appear in EPJ

Phase transitions for the Lifshitz black holes

We study possibility of phase transitions between Lifshitz black holes and other configurations by using free energies explicitly. A phase transition between Lifshitz soliton and Lifshitz black hole might not occur in three dimensions. We find that a phase transition between Lifshitz and BTZ black holes unlikely occurs because they have different asymptotes. Similarly, we point out that any phase transition between Lifshitz and black branes unlikely occurs in four dimensions since they have different asymptotes. This is consistent with a necessary condition for taking a phase transition in the gravitational system, which requires the same asymptote.Comment: 19 pages, 7 figures, a revised version to appear in EPJ

Slowly rotating black holes in the Horava-Lifshitz gravity

We investigate slowly rotating black holes in the Ho\v{r}ava-Lifshitz (HL) gravity. For $\Lambda_W=0$ and $\lambda=1$, we find a slowly rotating black hole of the Kehagias-Sfetsos solution in asymptotically flat spacetimes. We discuss their thermodynamic properties by computing mass, temperature, angular momentum, and angular velocity on the horizon.Comment: 12 pages, no figures, version to appear in EPJ

Concurrent Magnetic and Metal-Insulator Transitions in (Eu,Sm)B_6 Single Crystals

The effects of magnetic doping on a EuB_6 single crystal were investigated based on magnetic and transport measurements. A modest 5% Sm substitution for Eu changes the magnetic and transport properties dramatically and gives rise to concurrent antiferromagnetic and metal-insulator transitions (MIT) from ferromagnetic MIT for EuB6. Magnetic doping simultaneously changes the itinerant carrier density and the magnetic interactions. We discuss the origin of the concurrent magnetic MIT in (Eu,Sm)B_6.Comment: 13 pages, 3 figures, final version to appear in Appl. Phys. Lett