Critical collapse of collisionless matter - a numerical investigation

In recent years the threshold of black hole formation in spherically symmetric gravitational collapse has been studied for a variety of matter models. In this paper the corresponding issue is investigated for a matter model significantly different from those considered so far in this context. We study the transition from dispersion to black hole formation in the collapse of collisionless matter when the initial data is scaled. This is done by means of a numerical code similar to those commonly used in plasma physics. The result is that for the initial data for which the solutions were computed, most of the matter falls into the black hole whenever a black hole is formed. This results in a discontinuity in the mass of the black hole at the onset of black hole formation.Comment: 22 pages, LaTeX, 7 figures (ps-files, automatically included using psfig

Possible direct method to determine the radius of a star from the spectrum of gravitational wave signals

We computed the spectrum of gravitational waves from a dust disk star of radius R inspiraling into a Kerr black hole of mass M and specific angular momentum a. We found that when R is much larger than the wave length of the quasinormal mode, the spectrum has several peaks and the separation of peaks $\Delta\omega$ is proportional to $R^{-1}$ irrespective of M and a. This suggests that the radius of the star in coalescing binary black hole - star systems may be determined directly from the observed spectrum of gravitational wave. This also suggests that the spectrum of the radiation may give us important information in gravitational wave astronomy as in optical astronomy.Comment: 4 pages with 3 eps figures, revtex.sty, accepted for publication in Phys. Rev. Let

Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid

We observe critical phenomena in spherical collapse of radiation fluid. A sequence of spacetimes $\cal{S}[\eta]$ is numerically computed, containing models ($\eta\ll 1$) that adiabatically disperse and models ($\eta\gg 1$) that form a black hole. Near the critical point ($\eta_c$), evolutions develop a self-similar region within which collapse is balanced by a strong, inward-moving rarefaction wave that holds $m(r)/r$ constant as a function of a self-similar coordinate $\xi$. The self-similar solution is known and we show near-critical evolutions asymptotically approaching it. A critical exponent $\beta \simeq 0.36$ is found for supercritical ($\eta>\eta_c$) models.Comment: 10 pages (LaTeX) (to appear in Phys. Rev. Lett.), TAR-039-UN

The Dynamics of a Meandering River

We present a statistical model of a meandering river on an alluvial plane which is motivated by the physical non-linear dynamics of the river channel migration and by describing heterogeneity of the terrain by noise. We study the dynamics analytically and numerically. The motion of the river channel is unstable and we show that by inclusion of the formation of ox-bow lakes, the system may be stabilised. We then calculate the steady state and show that it is in agreement with simulations and measurements of field data.Comment: Revtex, 12 pages, 2 postscript figure

Head-on collisions of black holes: the particle limit

We compute gravitational radiation waveforms, spectra and energies for a point particle of mass $m_0$ falling from rest at radius $r_0$ into a Schwarzschild hole of mass $M$. This radiation is found to lowest order in $(m_0/M)$ with the use of a Laplace transform. In contrast with numerical relativity results for head-on collisions of equal-mass holes, the radiated energy is found not to be a monotonically increasing function of initial separation; there is a local radiated-energy maximum at $r_0\approx4.5M$. The present results, along with results for infall from infinity, provide a complete catalog of waveforms and spectra for particle infall. We give a representative sample from that catalog and an interesting observation: Unlike the simple spectra for other head-on collisions (either of particle and hole, or of equal mass holes) the spectra for $\infty>r_0>\sim5M$ show a series of evenly spaced bumps. A simple explanation is given for this. Lastly, our energy vs. $r_0$ results are compared with approximation methods used elsewhere, for small and for large initial separation.Comment: 15 pages, REVTeX, 25 figure

Collapse to Black Holes in Brans-Dicke Theory: I. Horizon Boundary Conditions for Dynamical Spacetimes

We present a new numerical code that evolves a spherically symmetric configuration of collisionless matter in the Brans-Dicke theory of gravitation. In this theory the spacetime is dynamical even in spherical symmetry, where it can contain gravitational radiation. Our code is capable of accurately tracking collapse to a black hole in a dynamical spacetime arbitrarily far into the future, without encountering either coordinate pathologies or spacetime singularities. This is accomplished by truncating the spacetime at a spherical surface inside the apparent horizon, and subsequently solving the evolution and constraint equations only in the exterior region. We use our code to address a number of long-standing theoretical questions about collapse to black holes in Brans-Dicke theory.Comment: 46 pages including figures, uuencoded gz-compressed postscript, Submitted to Phys Rev

Atomic micromotion and geometric forces in a triaxial magnetic trap

Non-adiabatic motion of Bose-Einstein condensates of rubidium atoms arising from the dynamical nature of a time-orbiting-potential (TOP) trap was observed experimentally. The orbital micromotion of the condensate in velocity space at the frequency of the rotating bias field of the TOP was detected by a time-of-flight method. A dependence of the equilibrium position of the atoms on the sense of rotation of the bias field was observed. We have compared our experimental findings with numerical simulations. The nonadiabatic following of the atomic spin in the trap rotating magnetic field produces geometric forces acting on the trapped atoms.Comment: 4 pages, 4 figure

Evolving Einstein's Field Equations with Matter: The ``Hydro without Hydro'' Test

We include matter sources in Einstein's field equations and show that our recently proposed 3+1 evolution scheme can stably evolve strong-field solutions. We insert in our code known matter solutions, namely the Oppenheimer-Volkoff solution for a static star and the Oppenheimer-Snyder solution for homogeneous dust sphere collapse to a black hole, and evolve the gravitational field equations. We find that we can evolve stably static, strong-field stars for arbitrarily long times and can follow dust sphere collapse accurately well past black hole formation. These tests are useful diagnostics for fully self-consistent, stable hydrodynamical simulations in 3+1 general relativity. Moreover, they suggest a successive approximation scheme for determining gravitational waveforms from strong-field sources dominated by longitudinal fields, like binary neutron stars: approximate quasi-equilibrium models can serve as sources for the transverse field equations, which can be evolved without having to re-solve the hydrodynamical equations (``hydro without hydro'').Comment: 4 postscript figures. Submitted to Phys. Rev. D15 as a Brief Repor

Nonadiabatic Dynamics of Atoms in Nonuniform Magnetic Fields

Dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, is considered by applying an accurate method for solving nonlinear systems of differential equations. This method is more general than the adiabatic approximation and, thus, permits to check the limits of the latter and also to analyze nonadiabatic regimes of motion. An unusual nonadiabatic regime is found when atoms are confined from one side of the z-axis but are not confined from another side. The lifetime of atoms in a trap in this semi-confining regime can be sufficiently long for accomplishing experiments with a cloud of such atoms. At low temperature, the cloud is ellipsoidal being stretched in the axial direction and moving along the z-axis. The possibility of employing the semi-confining regime for studying the relative motion of one component through another, in a binary mixture of gases is discussed.Comment: 1 file, 17 pages, RevTex, 2 table

Self-Similar Interpolation in Quantum Mechanics

An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar approximation theory. In order to derive interpolation formulae valid in the whole range of parameters of considered physical quantities, the self-similar renormalization procedure is complimented here by boundary conditions which define control functions guaranteeing correct asymptotic behaviour in the vicinity of boundary points. To emphasize the generality of the approach, it is illustrated by different problems that are typical for quantum mechanics, such as anharmonic oscillators, double-well potentials, and quasiresonance models with quasistationary states. In addition, the nonlinear Schr\"odinger equation is considered, for which both eigenvalues and wave functions are constructed.Comment: 1 file, 30 pages, RevTex, no figure