Alexander S. Silbergleit

“Stable” Quasi-periodic Oscillations and Black Hole Properties from Diskoseismology

We compare our calculations of the frequencies of the fundamental g-, c-, and p-modes of relativistic thin accretion disks with recent observations of high-frequency quasi-periodic oscillations (QPOs) in X-ray binaries with black hole candidates. These classes of modes encompass all adiabatic perturbations of such disks. The frequencies of these modes depend mainly on the mass and angular momentum of the black hole; their weak dependence on disk luminosity is also explicitly indicated. Identifying the recently discovered, relatively stable QPO pairs with the fundamental g- and c-modes provides a determination of the mass and angular momentum of the black hole. For GRO J1655-40, M = 5.9 ± 1.0 M☉ and J = (0.917 ± 0.024)GM2/c, in agreement with spectroscopic mass determinations. For GRS 1915+105, M = 42.4 ± 7.0 M☉ and J = (0.926 ± 0.020)GM2/c or (less favored) M = 18.2 ± 3.1 M☉ and J = (0.701 ± 0.043)GM2/c. We briefly address the issues of the amplitude, frequency width, and energy dependence of these QPOs.

Relativistic Diskoseismology. I. Analytical Results for “Gravity Modes”

We generalize previous calculations to a fully relativistic treatment of adiabatic oscillations that are trapped in the inner regions of accretion disks by non-Newtonian gravitational effects of a black hole. We employ the Kerr geometry within the scalar potential formalism of Ipser and Lindblom, neglecting the gravitational field of the disk. This approach treats perturbations of arbitrary stationary, axisymmetric, perfect fluid models. It is applied here to thin accretion disks. Approximate analytic eigenfunctions and eigenfrequencies are obtained for the most robust and observable class of modes, which corresponds roughly to the gravity (internal) oscillations of stars. The dependence of the oscillation frequencies on the mass and angular momentum of the black hole is exhibited. These trapped modes do not exist in Newtonian gravity, and thus provide a signature and probe of the strong-field structure of black holes. Our predictions are relevant to observations that could detect modulation of the X-ray luminosity from stellar mass black holes in our Galaxy and the UV and optical luminosity from supermassive black holes in active galactic nuclei.

Relativistic Diskoseismology. III. Low-Frequency Fundamental p-Modes

We extend our investigation of the normal modes of small adiabatic oscillations of relativistic barotropic thin accretion disks to the inertial-pressure (p) modes. We focus here on the lowest frequency fundamental p-modes, those with no axial or vertical nodes in their distribution. Through a variety of analyses, we obtain closed-form expressions for the eigenfrequencies and eigenfunctions. These depend on the luminosity and viscosity parameter of the disk as well as the mass and angular momentum of the black hole via detailed formulae for the speed of sound. The effect of a torque on the inner edge of the disk is also included. We compare the p-mode properties to those of the g- and c-modes.

Interplay between gravity and quintessence: a set of new GR solutions

Abstract A set of new exact analytical general relativity (GR) solutions with time-dependent and spatially inhomogeneous quintessence demonstrate (1) a static non-empty space–time with a horizon-type singular surface; (2) time-dependent spatially homogeneous ‘spheres’ which are completely different in geometry from the Friedmann isotropic models; (3) infinitely strong anti-gravity at a ‘true’ singularity where the density is infinitely large. It is also found that (4) the GR solutions allow for an extreme ‘density-free’ form of energy that can generate regular space–time geometries.

General Treatment of Orbiting GyroscopePrecession

We review the derivation of the metric for a spinning body of any shape andcomposition using linearized general relativity theory (LGRT), and also obtainthe same metric using a transformation argument. The latter derivation makes itclear that the linearized metric contains only the Eddington α and γ parameters,so no new parameter is involved in frame-dragging or Lense—Thirring effects.We then calculate the precession of an orbiting gyroscope in a general weakgravitational field described by a Newtonian potential (the gravitoelectric field)and a vector potential (the gravitomagnetic field). Next we make a multipoleanalysis of the potentials and the precession equations, giving all of these interms of the spherical harmonics moments of the density distribution. The analysisis not limited to an axially symmetric source, although the Earth, which is themain application, is very nearly axisymmetric. Finally, we analyze the precessionin regard to the Gravity Probe B (GP-B) experiment, and find that the effect ofthe Earths quadrupole moment (J2) on the geodetic precession is large enoughto be measured by GP-B (a previously known result), but the effect on theLense—Thirring precession is somewhat beyond the expected GP-B accuracy.

On the Energy-Momentum Tensor of the Scalar Field in Scalar–Tensor Theories of Gravity

We study the dynamical description of gravity, the appropriate definition of the scalar field energy-momentum tensor, and the interrelation between them in scalar-tensor theories of gravity. We show that the quantity which one would naively identify as the energy-momentum tensor of the scalar field is not appropriate because it is spoiled by a part of the dynamical description of gravity. A new connection can be defined in terms of which the full dynamical description of gravity is explicit, and the correct scalar field energy-momentum tensor can be immediately identified. Certain inequalities must be imposed on the two free functions (the coupling function and the potential) that define a particular scalar-tensor theory, to ensure that the scalar field energy density never becomes negative. The correct dynamical description leads naturally to the Einstein frame formulation of scalar-tensor gravity which is also studied in detail.

COROTATION RESONANCE AND DISKOSEISMOLOGY MODES OF BLACK HOLE ACCRETION DISKS

We demonstrate that the corotation resonance affects only some nonaxisymmetric g-mode oscillations of thin accretion disks, since it is located within their capture zones. Using a more general (weaker radial WKB approximation) formulation of the governing equations, such g-modes, treated as perfect fluid perturbations, are shown to formally diverge at the position of the corotation resonance. For the known g-modes with moderate values of the radial mode number and axial mode number (and any vertical mode number), the corotation resonance lies well outside their trapping region (and inside the innermost stable circular orbit), so the observationally relevant modes are unaffected by the resonance. The axisymmetric g-mode has been seen by Reynolds & Miller in a recent inviscid hydrodynamic accretion disk global numerical simulation. We also point out that the g-mode eigenfrequencies approximately obey the harmonic relation σ ∝ m for axial mode numbers | m| ≥ 1.

Explicit Green's function of a boundary value problem for a sphere and trapped flux analysis in Gravity Probe B experiment

Magnetic flux trapped on the surface of superconducting rotors of the Gravity Probe B (GP-B) experiment produces some signal in the superconducting quantum interference device readout. For the needs of GP-B error analysis and simulation of data reduction, this signal is calculated and analyzed in this article. We first solve a magnetostatic problem for a point source on the surface of a sphere, finding the closed form elementary expression for the corresponding Green’s function. Second, we calculate the flux through the pick-up loop as a function of the source position. Next, the time dependence of a source position, caused by rotor motion according to a symmetric top model, and thus the time signature of its flux are determined, and the spectrum of the trapped flux signal is analyzed. Finally, a multipurpose program of trapped flux signal generation based on the above results is described, various examples of the signal obtained by means of this program are given, and their features are discussed. Signals of up to 100 fluxons, i.e., 100 pairs of positive and negative point sources, are examined.

Shock waves and vorticity generation in protogalactic medium

A theory of secondary vorticity is suggested on grounds of an isotropic Hot Big Bang. Vortical motions are generated in front of the shock waves, which appear as a result of supersonic hydrodynamic processes induced by gravitational instability at a later epoch of cosmological expansion. Inside large layers of gas compressed by shocks subsonic turbulence with both vortical and acoustic modes develops. Every such layer may be treated as a protocluster; and eddies, if strong enough, would give rise to protogalaxies. An effective mechanism of vorticity generation — scattering of density inhomogeneities on shock fronts — is examined in detail. Quantitative estimates show that the vortices that are due to this mechanism can be at least the order of magnitude to account for the angular mometa of spiral galaxies. The spectrum of initial irrotational perturbations remains open to discussion, but characteristic amplitudes required do not contradict any observational or theoretical restrictions.

Potential and field singularity at a surface point charge

The behavior of the magnetic potential near a point charge (fluxon) located at a curved regular boundary surface is shown to be essentially different from that of a volume point charge. In addition to the usual inverse distance singularity, two singular terms are generally present. The first of them, a logarithmic one, is axially symmetric with respect to the boundary normal at the charge location, and proportional to the sum of the two principal curvatures of the boundary surface at this point, that is, to the local mean curvature. The second term is asymmetric and proportional to the difference of the two principal curvatures in question; it is also bounded at the charge location. Both terms vanish, apparently, if the charge is at a planar point of the boundary, and only in this case. The field in the charge vicinity behaves accordingly, featuring generally two singular terms proportional to the inverse distance, in addition to the main inverse distance squared singularity. This result is significant, in particular, for studying the interaction of magnetic vortices in type II superconductors.