Quasi-spherical Approximation Research Articles

Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates

Using a quasispherical approximation of an affine-null metric adapted to an asymptotic Bondi inertial frame, we present high order approximations of the metric functions in terms of the specific angular momentum for a slowly rotating stationary and axisymmetric vacuum spacetime. The metric is obtained by following the procedure of integrating the hierarchy of Einstein equations in a characteristic formulation utilizing master functions for the perturbations. It further verified its equivalence with the Kerr metric in the slowly rotating approximation by carrying out an explicit transformation between the Boyer-Lindquist coordinates to the employed affine-null coordinates. A peculiar feature of the derivation is that in the solution of the perturbation equations for every order a new integration constant appears which cannot be set to zero using asymptotical flatness or regularity arguments. However, these additional integration constants can be absorbed into the overall Komar mass and Komar angular momentum of a slowly rotating black hole.

Interaction of benzene with water and aqueous solutions of alkali metal chlorides

The balance of potential energies of compression and expansion of a water cavity containing a benzene molecule is calculated in the quasi-spherical approximation. It is established that the cavity expands under the action of reactive electrostatic repulsion forces and is compressed under the action of forces of macroscopic surface tension and dispersion interaction. It is shown that in the presence of ions disrupting the water structure, the cavity increases in size.

Pulsation-Driven Winds from High Luminosity Stars

Based on 1-dimensional numerical simulations including the rotational acceleration in a quasi-spherical approximation we present pulsation-driven mass loss from luminous stars. In particular, for our model WN8 with M = 60 M ๏ , L = 8×10 5 L ๏ and T eff = 25 000 K with a rotation rate of v sin i = 160 km s -1 given at the stellar photosphere of R p = 47.6 R ๏ and a stellar pulsation of P = 4.144 days we compute a time-dependent mass loss with an averaged rate of 1.28×10 -4 M ๏ /yr. Further implications of such theoretical models are briefly discussed for observations of variable stars with large amplitudes.

Rotating stellar models and dynamic tides in close binaries: A first approach

Rotating stellar models - homogeneous and evolved ones - were introduced for the first time, in order to investigate the effects of rotationally induced changes in the internal structure of stars on the apsidal motion in close binary systems within the framework of the theory of dynamic tides. The rotating models are calculated in the quasi-spherical approximation under the assumption that the star rotates as a solid body. The models show that the spectrum of resonances between dynamic tides and free oscillation modes is substantially modified by rotation. In particular, the changes in the internal structure of the rotating models yield complex spectra which are more than simple images of the spectra in non-rotating models shifted in the period space. An immediate consequence of the differences between rotating and non-rotating models is that a reconsideration of the global problem of the apsidal-motion may be in order.

Gravitational-wave dynamics and black-hole dynamics: second quasi-spherical approximation

Gravitational radiation with roughly spherical wavefronts, produced by roughly spherical black holes or other astrophysical objects, is described by an approximation scheme. The first quasi-spherical approximation, describing radiation propagation on a background, is generalized to include additional non-linear effects, due to the radiation itself. The gravitational radiation is locally defined and admits an energy tensor, satisfying all standard local energy conditions and entering the truncated Einstein equations as an effective energy tensor. This second quasi-spherical approximation thereby includes gravitational radiation reaction, such as the back-reaction on the black hole. With respect to a canonical flow of time, the combined energy–momentum of the matter and gravitational radiation is covariantly conserved. The corresponding Noether charge is a local gravitational mass-energy. Energy conservation is formulated as a local first law relating the gradient of the gravitational mass to work and energy-supply terms, including the energy flux of the gravitational radiation. Zeroth, first and second laws of black-hole dynamics are given, involving a dynamic surface gravity. Local gravitational-wave dynamics is described by a non-linear wave equation. In terms of a complex gravitational-radiation potential, the energy tensor has a scalar-field form and the wave equation is an Ernst equation, holding independently at each spherical angle. The strain to be measured by a distant detector is simply defined.

Quasispherical approximation for rotating black holes

We numerically implement a quasispherical approximation scheme for computing gravitational waveforms for coalescing black holes, testing it against angular momentum by applying it to Kerr black holes. As error measures, we take the conformal strain and specific energy due to spurious gravitational radiation. The strain is found to be monotonic rather than wavelike. The specific energy is found to be at least an order of magnitude smaller than the 1% level expected from typical black-hole collisions, for angular momentum up to at least 70% of the maximum, for an initial surface as close as $r=3m.$

Gravitational waves from quasispherical black holes

A quasi-spherical approximation scheme, intended to apply to coalescing black holes, allows the waveforms of gravitational radiation to be computed by integrating ordinary differential equations.

Numerical models of giant planet formation with rotation

We present models of giant planet formation including the accretion and transport of angular momentum. The calculations are carried out in a one-dimensional quasispherical approximation, assuming hydrostatic equilibrium. The approximation of quasisphericity limits the calculations to relatively slowly rotating models. As in previous calculations without rotation (Bodenheimer and Pollack 1986), the so-called “core-accretion” model is adopted. Angular momentum transport is included for both radiative and convective zones. Convective regions are not forced to rotate uniformly at all times, but the angular momentum distribution in those regions is driven to uniform rotation, with transport coefficients based on mixing-length theory. Radiative regions whose angular momentum distributions are unstable according to the Goldreich-Schubert-Fricke criterion are driven to states of marginal stability, on timescales derived from linear theory and previous hydrodynamical modeling. The calculations are carried up to masses approximately equal to that of Saturn. Angular momentum transport is highly effective, producing models with a strong concentration of angular momentum in the outer convective zones that develop at envelope masses above 30 M +. Near the end of the calculation, gas accretion was turned off, and the models allowed to contract. The ratio of centrifugal force to gravity at the outer radius then rises high enough to validate the quasispherical approximation. At that point, mass is assumed to be shed to form a disk. We find that ∼1 M +, and ∼80% of the angular momentum, are lost to a disk. Such values of disk mass and angular momentum are amply sufficient for satellite system formation. As a result of the loss of angular momentum, however, the final planetary models have only one-third to one-half the present-day value of angular momentum of Saturn, indicating that yet larger amounts of angular momentum may have been present during formation.