Том 62, № 7 (2018)

The role of pressure as a source of gravity in general relativity is considered. In homogeneous, anisotropic cosmological models, the anisotropic pressure components along different coordinate axes are included as terms in the equations determining the accelerations along these axes; in this sense, this situation is similar to how the mass density is included in these equations. A change in the pressure component along one of the coordinates leads to an anisotropic change in the accelerations along all three coordinates. However, the pressure components are not present in the equation determining the initial conditions. On the other hand, with an inhomogeneous matter density distribution, the mass density and pressure play fundamentally different roles as sources of gravity. The consequences of this are considered.

The influence of aberration on the observational parameters of radio jets and estimates of their physical properties is studied. Aberration distorts the apparent shapes of radio sources. Two identical relativistic jets (whose spectra have maxima) moving approximately along the line of sight could be observed as a compact GPS radio source (jet) and an extended source with a power-law spectrum (counterjet). The apparent flux densities, shapes, and spectra of relativistic radio jets are distorted even when the jets lie in the plane of the sky (across the line of sight). Exact formulas are derived for the estimated physical parameters of relativistic radio jets, taking into account aberration.

Approaches used in modern numerical simulations of the dynamics of dust and gas in circumstellar disks are tested. The gas and dust are treated like interpenetrating continuous media that can exchange momentum. A stiff coupling between the gas and dust phases is typical for such disks, with the dust stopping time much less than the characteristic dynamical time scale. This imposes high demands on the methods used to simulate the dust dynamics. A grid-based, piecewise-parabolic method is used as the basic algorithm for solving the gas-dynamical equations. Numerical solutions obtained using various methods to compute the momentum exchanges are presented for the case of monodisperse dust. Numerical solutions are obtained for shock tube problem and the propagation of sound waves in a gas–dust medium. The studied methods are compared in terms of their ability to model media with (a) an arbitrary (short or long) dust stopping time, and (b) an arbitrary dust concentration in the gas (varying the dust to gas mass ratio from 0.01 to 1). A method for computing the momentum exchange with infinite-order accuracy in time is identified, which makes it possible to satisfy the conditions (a) and (b) with minimal computational costs. A first-order method that shows similar results in the test computations is also presented. It is shown that the proposed first-order method for monodisperse dust can be extended to a regime when the dust is polydisperse; i.e., a regime represented by several fractions with different stopping times. Formulas for computing the gas and dust velocities for polydisperse dust with each fraction exchanging momentum with the gas are presented.