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

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>

Patch effect in drag-free satelites

To compensate for the non–gravitational 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

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

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