Formation of a sonic horizon in isotropically expanding Bose-Einstein condensates

We propose a simple experiment to create a sonic horizon in isotropically trapped cold atoms within currently available experimental techniques. Numerical simulation of the Gross-Pitaevskii equation shows that the sonic horizon should appear by making the condensate expand. The expansion is triggered by changing the interaction which can be controlled by the Feshbach resonance in real experiments. The sonic horizon is shown to be quasi-static for sufficiently strong interaction or large number of atoms. The characteristic temperature that is associated with particle emission from the horizon, which corresponds to the Hawking temperature in an ideal situation, is estimated to be a few nK.Comment: 7 pages, 8 figures; Final version, accepted to Phys.Rev.

Dynamical instability in a relativistic cylindrical shell composed of counter rotating particles

We give a perturbative analysis for an infinitesimally thin cylindrical shell composed of counter rotating collisionless particles, originally devised by Apostolatos and Thorne. They found a static solution of the shell and concluded by C-energy argument that it is stable. Recently, the present authors and Ida reanalyzed this system by evaluating the C-energy on the future null infinity and found that the system has an instability, though it was not shown how the system is unstable. In this paper, it is shown in the framework of the linear perturbation theory that, if the constituent particles move slowly, the static shell is unstable in the sense that the perturbation of its circumferential radius oscillates with exponentially growing amplitude, whereas if the speed of the constituent particle exceeds a critical value, the shell just expands or contracts exponentially with time.Comment: 21 pages, 7 figure

Particle creation in Bose--Einstein condensates: Theoretical formulation based on conserving gapless mean field theory

We formulate particle creation phenomena in Bose--Einstein condensates in terms of conserving gapless mean field theory for weakly interacting Bose gases. The particle creation spectrum is calculated by rediagonalizing the Bogoliubov--de Gennes (BdG) Hamiltonian in mean field theory. The conservation implies that quasiparticle creation is accompanied by quantum backreaction to the condensates. Particle creation in this mean field theory is found to be equivalent to that in quantum field theory (QFT) in curved spacetime. An expression is obtained for an effective metric affected by quantum backreaction. The formula for the particle creation spectrum obtained in terms of QFT in curved spacetime is shown to be the same as that given by rediagonalizing the BdG Hamiltonian.Comment: 9 pages, typos correcte

Naked singularity resolution in cylindrical collapse

In this paper, we study the gravitational collapse of null dust in the cylindrically symmetric spacetime. The naked singularity necessarily forms at the symmetry axis. We consider the situation in which null dust is emitted again from the naked singularity formed by the collapsed null dust and investigate the back-reaction by this emission for the naked singularity. We show a very peculiar but physically important case in which the same amount of null dust as that of the collapsed one is emitted from the naked singularity as soon as the ingoing null dust hits the symmetry axis and forms the naked singularity. In this case, although this naked singularity satisfies the strong curvature condition by Kr\'{o}lak (limiting focusing condition), geodesics which hit the singularity can be extended uniquely across the singularity. Therefore we may say that the collapsing null dust passes through the singularity formed by itself and then leaves for infinity. Finally the singularity completely disappears and the flat spacetime remains.Comment: 17 pages, no figur

Quasinormal Ringing for Acoustic Black Holes at Low Temperature

We investigate a condensed matter ``black hole'' analogue, taking the Gross-Pitaevskii (GP) equation as a starting point. The linearized GP equation corresponds to a wave equation on a black hole background, giving quasinormal modes under some appropriate conditions. We suggest that we can know the detailed characters and corresponding geometrical information about the acoustic black hole by observing quasinormal ringdown waves in the low temperature condensed matters.Comment: 9 pages, 3 figures, PRD accepted versio

Thermodynamics of Squashed Kaluza-Klein Black Holes and Black Strings -- A Comparison of Reference Backgrounds --

We investigate thermodynamics constructed on different background reference spacetimes for squashed Kaluza-Klein (SqKK) black hole and electrically charged black string in five-dimensional Einstein-Maxwell system. Two spacetimes are possible to be reference spacetimes giving finite gravitational classical actions: one is four-dimensional Minkowski times a circle and the other is the KK monopole. The boundary of the SqKK black hole can not be matched perfectly to that of the former reference spacetime because of the difference in topology. However, the resultant classical action coincides with that calculated by the counterterm subtraction scheme. The boundary of the KK monopole has the same topology with that of the SqKK black hole and can be matched to the boundary of the black hole perfectly. The resultant action takes different value from the result given by using the former reference spacetime. After a brief review of thermodynamic quantities of the black hole solutions, we calculate thermodynamic potentials relevant for several thermodynamic environments. The most stable state is different for each environment: For example, the KK monopole is the most stable state in isothermal environment with fixed gravitational tension. On the other hand, when the size of the extra-dimension is fixed, the Minkowski times a circle is the most stable. It is shown that these two spacetimes can be reference spacetimes of the five-dimensional black string.Comment: 28 pages; references added, typo corrected;version accepted for publication in Class. Quantum Gra