Black holes and rotation

In this article, we first consider briefly the basic properties of the non-rotating Schwarzschild black hole and the rotating Kerr black hole Rotational effects are then described in static and stationary spacetimes with arial symmetry by studying inertial forces, gyroscopic precession and gravi-electromagnetism. The results are applied to the black hole spacetimes

Black Holes in Non-flat Backgrounds: the Schwarzschild Black Hole in the Einstein Universe

As an example of a black hole in a non-flat background a composite static spacetime is constructed. It comprises a vacuum Schwarzschild spacetime for the interior of the black hole across whose horizon it is matched on to the spacetime of Vaidya representing a black hole in the background of the Einstein universe. The scale length of the exterior sets a maximum to the black hole mass. To obtain a non-singular exterior, the Vaidya metric is matched to an Einstein universe. The behaviour of scalar waves is studied in this composite model.Comment: 8 pages, 3 postscript figures, minor corrections Journal Ref: accepted for Physical Review

The dynamics of condensate shells: collective modes and expansion

We explore the physics of three-dimensional shell-shaped condensates, relevant to cold atoms in "bubble traps" and to Mott insulator-superfluid systems in optical lattices. We study the ground state of the condensate wavefunction, spherically-symmetric collective modes, and expansion properties of such a shell using a combination of analytical and numerical techniques. We find two breathing-type modes with frequencies that are distinct from that of the filled spherical condensate. Upon trap release and subsequent expansion, we find that the system displays self-interference fringes. We estimate characteristic time scales, degree of mass accumulation, three-body loss, and kinetic energy release during expansion for a typical system of Rb87

Scalar Deformations of Schwarzschild Holes and Their Stability

We construct two solutions of the minimally coupled Einstein-scalar field equations, representing regular deformations of Schwarzschild black holes by a self-interacting, static, scalar field. One solution features an exponentially decaying scalar field and a triple-well interaction potential; the other one is completely analytic and sprouts Coulomb-like scalar hair. Both evade the no-hair theorem by having partially negative potential, in conflict with the dominant energy condition. The linear perturbation theory around such backgrounds is developed in general, and yields stability criteria in terms of effective potentials for an analog Schr\"odinger problem. We can test for more than half of the perturbation modes, and our solutions prove to be stable against those.Comment: 24 pp, 16 figs, Latex; version published in Int. J. Mod. Phys.

Coexistence of superfluid and Mott phases of lattice bosons

Recent experiments on strongly-interacting bosons in optical lattices have revealed the co-existence of spatially-separated Mott-insulating and number-fluctuating phases. The description of this inhomogeneous situation is the topic of this Letter. We establish that the number-fluctuating phase forms a superfluid trapped between the Mott-insulating regions and derive the associated collective mode structure. We discuss the interlayer's crossover between two- and three-dimensional behavior as a function of the lattice parameters and estimate the critical temperatures for the transition of the superfluid phase to a normal phase

Double-gap superconducting proximity effect in nanotubes

We theoretically explore the possibility of a superconducting proximity effect in single-walled metallic carbon nanotubes due to the presence of a superconducting substrate. An unconventional double-gap situation can arise in the two bands for nanotubes of large radius wherein the tunneling is (almost) symmetric in the two sublattices. In such a case, a proximity effect can take place in the symmetric band below a critical experimentally-accessible Coulomb interaction strength in the nanotube. Furthermore, due to interactions in the nanotube, the appearance of a BCS gap in this band stabilizes superconductivity in the other band at lower temperatures. We also discuss the scenario of highly asymmetric tunneling and show that this case too supports double-gap superconductivity.Comment: 4 pages, 2 figure

Dirac Quasinormal modes of Schwarzschild black hole

The quasinormal modes (QNMs) associated with the decay of Dirac field perturbation around a Schwarzschild black hole is investigated by using continued fraction and Hill-determinant approaches. It is shown that the fundamental quasinormal frequencies become evenly spaced for large angular quantum number and the spacing is given by $\omega_{\lambda+1}- \omega_{\lambda}=0.38490-0.00000i$. The angular quantum number has the surprising effect of increasing real part of the quasinormal frequencies, but it almost does not affect imaginary part, especially for low overtones. In addition, the quasinormal frequencies also become evenly spaced for large overtone number and the spacing for imaginary part is $Im(\omega_{n+1})-Im(\omega_n)\approx -i/4M$ which is same as that of the scalar, electromagnetic, and gravitational perturbations.Comment: 14 pages, 5 figure