26 research outputs found

### Global Dynamics of Cosmological Expansion with Minimally Coupled Scalar Field

We give a complete description of the asymptotic behavior of a
Friedmann-Robertson-Walker Universe with ``normal'' matter and a minimally
coupled scalar field. We classify the conditions under which the Universe is or
is not accelerating. In particular, we show that only two types of large time
behavior exist: an exponential regime, and a subexponential expansion with the
logarithmic derivative of the scale factor tending to zero. In the case of the
subexponetial expansion the Universe accelerates when the scalar field energy
density is dominant and the potential behaves in a specified manner, or if
matter violates the strong energy conditon $\rho + 3p >0$. When the expansion
is exponential the Universe accelerates, and the scalar field energy density is
dominant. We also find that the existence of the Big Bang and a never ending
expansion of the Universe constrain the equation of state of matter at large
and small densities, respectively.Comment: Submitte to Phys. Lett. A. Minor changes were made to clarify some
point

### 'Stable' QPOs 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 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 only 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\pm 1.0 M_\sun,
$J=(0.917\pm 0.024)GM^2/c$, in agreement with spectroscopic mass
determinations. For GRS 1915+105, M=42.4\pm 7.0 M_\sun, $J=(0.926\pm
0.020)GM^2/c$ or (less favored) M=18.2\pm 3.1 M_\sun, $J=(0.701\pm
0.043)GM^2/c$. We briefly address the issues of the amplitude, frequency width,
and energy dependence of these QPOs.Comment: 10 pages, 1 figure. Accepted for publication in Astrophysical Journal
Letter

### Corotation Resonance and Diskoseismology Modes of Black Hole Accretion Disks

We demonstrate that the corotation resonance affects only some
non-axisymmetric 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. A small amount of viscosity adds a small imaginary
part to the eigenfrequency which has been shown to induce a secular instability
(mode growth) if it acts hydrodynamically. The g-mode corotation resonance
divergence disappears, but the mode magnitude can remain largest at the place
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 are
approximately proportional to m for axial mode numbers |m|>0.Comment: 16 pages, no figures. Submitted to The Astrophysical Journa

### Patch effect in drag-free satelites

To compensate for the nonâgravitational orbital disturbances drag free satellites monitor and control their position with respect to a reference body enclosed inside their structure. The body, shielded from the environment, follows a free fall trajectory when its motion can be ideally considered decoupled from that of the spacecraft. Lessons learned from Gravity Probe B and the design of the Satellite Test of the Equivalence Principle experiment strongly motivate the study of the force and torque between the reference body and the spacecraft due to uneven distributions of electrostatic potentials. Additional interest to that comes also from prospective space experiments as Microscope and the Laser Interferometer Space Antenna

### Relativistic Diskoseismology. I. Analytical Results for 'Gravity Modes'

We generalize previous calculations to a fully relativistic treatment of
adiabatic oscillations which 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 which
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.Comment: 31 pages, 6 figures, uses style file aaspp4.sty, prepared with the
AAS LATEX macros v4.0, significant revision of earlier submission to include
modes with axial index m>

### Electrostatic Patch Effect in Cylindrical Geometry. III. Torques

We continue to study the effect of uneven voltage distribution on two close
cylindrical conductors with parallel axes started in our papers [1] and [2],
now to find the electrostatic torques. We calculate the electrostatic potential
and energy to lowest order in the gap to cylinder radius ratio for an arbitrary
relative rotation of the cylinders about their symmetry axis. By energy
conservation, the axial torque, independent of the uniform voltage difference,
is found as a derivative of the energy in the rotation angle. We also derive
both the axial and slanting torques by the surface integration method: the
torque vector is the integral over the cylinder surface of the cross product of
the electrostatic force on a surface element and its position vector. The
slanting torque consists of two parts: one coming from the interaction between
the patch and the uniform voltages, and the other due to the patch interaction.
General properties of the torques are described. A convenient model of a
localized patch suggested in [2] is used to calculate the torques explicitly in
terms of elementary functions. Based on this, we analyze in detail patch
interaction for one pair of patches, namely, the torque dependence on the patch
parameters (width and strength) and their mutual positions. The effect of the
axial torque is then studied for the experimental conditions of the STEP
mission.Comment: 28 pages, 6 Figures. Submitted to Classical Quantum Gravit

### 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.Comment: Submitted to Phys. Rev D15, 10 pages. Uses ReVTeX macro

### Electrostatic Patch Effect in Cylindrical Geometry. I. Potential and Energy between Slightly Non-Coaxial Cylinders

We study the effect of any uneven voltage distribution on two close
cylindrical conductors with parallel axes that are slightly shifted in the
radial and by any length in the axial direction. The investigation is
especially motivated by certain precision measurements, such as the Satellite
Test of the Equivalence Principle (STEP). By energy conservation, the force can
be found as the energy gradient in the vector of the shift, which requires
determining potential distribution and energy in the gap. The boundary value
problem for the potential is solved, and energy is thus found to the second
order in the small transverse shift, and to lowest order in the gap to cylinder
radius ratio. The energy consists of three parts: the usual capacitor part due
to the uniform potential difference, the one coming from the interaction
between the voltage patches and the uniform voltage difference, and the energy
of patch interaction, entirely independent of the uniform voltage. Patch effect
forces and torques in the cylindrical configuration are derived and analyzed in
the next two parts of this work.Comment: 26 pages, 1 Figure. Submitted to Classical and Quantum Gravit

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### Normal Modes of Black Hole Accretion Disks

This paper studies the hydrodynamical problem of normal modes of small adiabatic oscillations of relativistic barotropic thin accretion disks around black holes (and compact weakly magnetic neutron stars). Employing WKB techniques, we obtain the eigen frequencies and eigenfunctions of the modes for different values of the mass and angular momentum of the central black hole. We discuss the properties of the various types of modes and examine the role of viscosity, as it appears to render some of the modes unstable to rapid growth