Computing radiation from Kerr black holes: Generalization of the Sasaki-Nakamura equation

As shown by Teukolsky, the master equation governing the propagation of weak radiation in a black hole spacetime can be separated into four ordinary differential equations, one for each spacetime coordinate. (``Weak'' means the radiation's amplitude is small enough that its own gravitation may be neglected.) Unfortunately, it is difficult to accurately compute solutions to the separated radial equation (the Teukolsky equation), particularly in a numerical implementation. The fundamental reason for this is that the Teukolsky equation's potentials are long ranged. For non-spinning black holes, one can get around this difficulty by applying transformations which relate the Teukolsky solution to solutions of the Regge-Wheeler equation, which has a short-ranged potential. A particularly attractive generalization of this approach to spinning black holes for gravitational radiation (spin weight s = -2) was given by Sasaki and Nakamura. In this paper, I generalize Sasaki and Nakamura's results to encompass radiation fields of arbitrary integer spin weight, and give results directly applicable to scalar (s = 0) and electromagnetic (s = -1) radiation. These results may be of interest for studies of astrophysical radiation processes near black holes, and of programs to compute radiation reaction forces in curved spacetime.Comment: 10 pages, no figures, to appear in Phys. Rev. D. Present version updates the references, fixes some typos, and corrects some of the Introductory tex

Disorder, pseudospins, and backscattering in carbon nanotubes

We address the effects of disorder on the conducting properties of metal and semiconducting carbon nanotubes. Experimentally, the mean free path is found to be much larger in metallic tubes than in doped semiconducting tubes. We show that this result can be understood theoretically if the disorder potential is long-ranged. The effects of a pseudospin index that describes the internal sublattice structure of the states lead to a suppression of scattering in metallic tubes, but not in semiconducting tubes. This conclusion is supported by tight-binding calculations.Comment: four page

Superconducting Properties under Magnetic Field in Na0.35_{0.35}CoO2⋅1.3_{2}{\cdot}1.3H2_{2}O Single Crystal

We report the in-plane resistivity and magnetic susceptibility of the layered cobalt oxide Na$_{0.35}$CoO$_{2}{\cdot}1.3$H$_{2}$O single crystal. The temperature dependence of the resistivity shows metallic behavior from room temperature to the superconducting transition temperature $T_{c}$ of 4.5 K. Sharp resistive transition, zero resistivity and almost perfect superconducting volume fraction below $T_{c}$ indicate the good quality and the bulk superconductivity of the single crystal. The upper critical field $H_{c2}$ and the coherence length $\xi$ are obtained from the resistive transitions in magnetic field parallel to the c-axis and the $ab$-plane. The anisotropy of $\xi$, $\xi_{ab} / \xi_{c} =$ 12 nm/1.3 nm $\simeq$ 9.2, suggests that this material is considered to be an anisotropic three dimensional superconductor. In the field parallel to the $ab$-plane, $H_{c2}$ seems to be suppressed to the value of Pauli paramagnetic limit. It may indicate the spin singlet superconductivity in the cobalt oxide.Comment: 4 pages, 4 figure

Enhancement of the upper critical field and a field-induced superconductivity in antiferromagnetic conductors

We propose a mechanism by which the paramagnetic pair-breaking effect is largely reduced in superconductors with coexisting antiferromagnetic long- range and short-range orders. The mechanism is an extension of the Jaccarino and Peter mechanism to antiferromagnetic conductors, but the resultant phase diagram is quite different. In order to illustrate the mechanism, we examine a model which consists of mobile electrons and antiferromagnetically correlated localized spins with Kondo coupling between them. It is found that for weak Kondo coupling, the superconductivity occurs over an extraordinarily wide region of the magnetic field including zero field. The critical field exceeds the Chandrasekhar and Clogston limit, but there is no lower limit in contrast to the Jaccarino and Peter mechanism. On the other hand, for strong Kondo coupling, both the low-field superconductivity and a field-induced superconductivity occur. Possibilities in hybrid ruthenate cuprate superconductors and some organic superconductors are discussed.Comment: 5 pages, 1 figure, revtex.sty, to be published in J.Phys.Soc.Jpn. Vol.71, No.3 (2002

Fermion scattering by a Schwarzschild black hole

We study the scattering of massive spin-half waves by a Schwarzschild black hole using analytical and numerical methods. We begin by extending a recent perturbation theory calculation to next order to obtain Born series for the differential cross section and Mott polarization, valid at small couplings. We continue by deriving an approximation for glory scattering of massive spinor particles by considering classical timelike geodesics and spin precession. Next, we formulate the Dirac equation on a black hole background, and outline a simple numerical method for finding partial wave series solutions. Finally, we present our numerical calculations of absorption and scattering cross sections and polarization, and compare with theoretical expectations.Comment: Minor changes, 1 figure added. Version to appear in Phys. Rev. D. 36 pages, 13 figure

Gate-Voltage Studies of Discrete Electronic States in Al Nanoparticles

We have investigated the spectrum of discrete electronic states in single, nm-scale Al particles incorporated into new tunneling transistors, complete with a gate electrode. The addition of the gate has allowed (a) measurements of the electronic spectra for different numbers of electrons in the same particle, (b) greatly improved resolution and qualitatively new results for spectra within superconducting particles, and (c) detailed studies of the gate-voltage dependence of the resonance level widths, which have directly demonstrated the effects of non-equilibrium excitations.Comment: 4 pages, 7 figure

Colloquium: Nonlinear collective interactions in quantum plasmas with degenerate electron fluids

The current understanding of some important nonlinear collective processes in quantum plasmas with degenerate electrons is presented. After reviewing the basic properties of quantum plasmas, we present model equations (e.g. the quantum hydrodynamic and effective nonlinear Schr\"odinger-Poisson equations) that describe collective nonlinear phenomena at nanoscales. The effects of the electron degeneracy arise due to Heisenberg's uncertainty principle and Pauli's exclusion principle for overlapping electron wavefunctions that result in tunneling of electrons and the electron degeneracy pressure. Since electrons are Fermions (spin-1/2), there also appears an electron spin current and a spin force acting on electrons due to the Bohr magnetization. The quantum effects produce new aspects of electrostatic (ES) and electromagnetic (EM) waves in a quantum plasma that are summarized in here. Furthermore, we discuss nonlinear features of ES ion waves and electron plasma oscillations (ESOs), as well as the trapping of intense EM waves in quantum electron density cavities. Specifically, simulation studies of the coupled nonlinear Schr\"odinger (NLS) and Poisson equations reveal the formation and dynamics of localized ES structures at nanoscales in a quantum plasma. We also discuss the effect of an external magnetic field on the plasma wave spectra and develop quantum magnetohydrodynamic (Q-MHD) equations. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects, in plasma-assisted nanotechnology, and in the next-generation of intense laser-solid density plasma interaction experiments.Comment: 25 pages, 14 figures. To be published in Reviews of Modern Physic

Equilibrium configurations of fluids and their stability in higher dimensions

We study equilibrium shapes, stability and possible bifurcation diagrams of fluids in higher dimensions, held together by either surface tension or self-gravity. We consider the equilibrium shape and stability problem of self-gravitating spheroids, establishing the formalism to generalize the MacLaurin sequence to higher dimensions. We show that such simple models, of interest on their own, also provide accurate descriptions of their general relativistic relatives with event horizons. The examples worked out here hint at some model-independent dynamics, and thus at some universality: smooth objects seem always to be well described by both ``replicas'' (either self-gravity or surface tension). As an example, we exhibit an instability afflicting self-gravitating (Newtonian) fluid cylinders. This instability is the exact analogue, within Newtonian gravity, of the Gregory-Laflamme instability in general relativity. Another example considered is a self-gravitating Newtonian torus made of a homogeneous incompressible fluid. We recover the features of the black ring in general relativity.Comment: 42 pages, 11 Figures, RevTeX4. Accepted for publication in Classical and Quantum Gravity. v2: Minor corrections and references adde

Area Spectrum of Kerr and extremal Kerr Black Holes from Quasinormal Modes

Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of Kerr and extremal Kerr black holes. Based on the proposal by Bekenstein and others that the black hole area spectrum is discrete and equally spaced, we implement Kunstatter's method to derive the area spectrum for the Kerr and extremal Kerr black holes. The real part of the quasinormal frequencies of Kerr black hole used for this computation is of the form $m\Omega$ where $\Omega$ is the angular velocity of the black hole horizon. The resulting spectrum is discrete but not as expected uniformly spaced. Thus, we infer that the function describing the real part of quasinormal frequencies of Kerr black hole is not the correct one. This conclusion is in agreement with the numerical results for the highly damped quasinormal modes of Kerr black hole recently presented by Berti, Cardoso and Yoshida. On the contrary, extremal Kerr black hole is shown to have a discrete area spectrum which in addition is evenly spaced. The area spacing derived in our analysis for the extremal Kerr black hole area spectrum is not proportional to $\ln 3$. Therefore, it does not give support to Hod's statement that the area spectrum $A_{n}=(4l^{2}_{p}ln 3)n$ should be valid for a generic Kerr-Newman black hole.Comment: 10 pages, no figure, LaTeX; v2: 12 pages, clarifying comments and an Appendix are added, version to appear in Mod. Phys. Lett.

Negative modes in the four-dimensional stringy wormholes

We study the Giddings-Strominger wormholes in string theories. We found negative modes among O(4)-symmetric fluctuations about the non-singular wormhole background. Hence the stringy wormhole contribution to the euclidean functional integral is purely imaginary. This means that the stringy wormhole is a bounce (not an instanton) and describes the nucleation and growth of wormholes in the Minkowski spacetime.Comment: 12 pages 2 figures, RevTe