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We investigate the properties of dark matter (DM) distribution in spiral galaxy U5750, employing the well known and widely used phenomenological density profiles such as pseudo-isothermal, Burkert, Navarro-Frenk-White, Einasto, Moore and exponential sphere. For simplicity we assume that DM distribution is spherically symmetric without accounting for the complex internal structure of the galaxy. We fit the rotation curve observational data of galaxy U5750 for each profile. We infer the model free parameters and estimate the total DM mass, and compare them with those reported in the literature. To discriminate the best fit profile among the considered ones, we make use of the Bayesian Information Criterion (BIC). On the basis of the performed statistical analysis, we provide physical interpretations for choosing certain profiles. In addition, by assuming that DM possesses non-zero pressure, we solve the Newtonian hydrostatic equilibrium equation and construct the pressure profiles as a functionof the radial coordinate for each above mentioned profile. Combining the density profiles with the pressure profiles we obtain equations of state for the DM in the considered galaxy. Further, we calculate the speed of soundin the DM medium and show that it behaves not unequivocally for the adopted profiles, though it decreaseswith an increasing DM density. Finally, we calculate the refracting index and discuss about astrophysical implications of the obtained results.

A Friedmann cosmological model, generalized to the epoch of dominance of dark matter, is considered. Its equation of state is chosen in a new, nonstationary form. Basing our approach on the process of light propagation in such a metric, we have found its refractive index, which turns out to be a constant quantity (or more accurately, one that depends on the epoch of the end of dominance of dark matter) and predict a possible effect of a burst of incoming radiation.

Here processes of wave propagation in a two-component Biot’s medium are considered which are generated by periodic forces actions. By use Fourier transformation of generalized functions, the Green tensor - a fundamental solutions of oscillation equations of this medium has been constructed. This tensor describes the process of propagation of harmonic waves of a fixed frequency in spaces of dimension N = 1,2,3 under the action of power sources concentrated at the coordinates origin, described by a singular delta -function. Based on it, generalized solutions of these equations are constructed under the action of various sources of periodic perturbations, which are described by both regular and singular generalized functions. For regular acting forces, integral representations of solutions are given that can be used to calculate the stress-strain state of a porous water-saturated medium.

We consider the circular motion of test particles in the gravitational field of a static and axially-symmetric compact object described by the $q$-metric. To this end, we calculate orbital parameters of test particles on accretion disks such as angular velocity ($\Omega$), total energy ($E$), angular momentum ($L$), and radius of the innermost stable circular orbit ($r_{ISCO}$) as functions of the mass ($m$) and quadrupole ($q$) parameters of the source. The radiative flux, differential, and spectral luminosity of the accretion disk, which are quantities that can be experimentally measured, are then explored in detail. The obtained results are compared with the corresponding ones for the Schwarzschild and Kerr black holes in order to establish whether black holes may be distinguished from the $q$-metric via observations of the accretion disk's spectrum., Comment: 10 pages, 8 figures