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 ($\mathrm{\Omega }$), total energy ($E$), angular momentum ($L$), and radius of the innermost stable circular orbit ($r_{\mathrm{ISCO}}$) 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.

We investigate the luminosity of the accretion disk of a static black hole surrounded by dark matter with anisotropic pressure. We calculate all basic orbital parameters of test particles in the accretion disk, such as angular velocity, angular momentum, energy, and radius of the innermost circular stable orbit as functions of the dark matter density, radial pressure, and anisotropic parameter, which establishes the relationship between the radial and tangential pressures. We show that the presence of dark matter with anisotropic pressure makes a noticeable difference in the geometry around a Schwarzschild black hole, affecting the radiative flux, differential luminosity, and spectral luminosity of the accretion disk.

We study the motion of test particles in the gravitational field of a Schwarzschild black hole surrounded by a spherical dark matter cloud with nonzero tangential pressure, and compute the luminosity of the accretion disk. The presence of nonvanishing tangential pressure allows us to mimic the dark matter’s angular momentum, while still considering a static model, which simplifies the mathematical framework. We compare the numerical results of the influence of dark matter on the luminosity of the accretion disks around static supermassive black holes with the previously studied cases of isotropic and anisotropic pressures. We show that the flux and luminosity of the accretion disk in the presence of dark matter are different from the case of a Schwarzschild black hole in a vacuum, and highlight the impact of the presence of tangential pressures.

We study thin accretion disks in the gravitational field of a class of rotating regular black holes. Our objective is to determine the key parameters governing these accretion disks: the radius of the innermost stable circular orbit $$(r_{\textrm{ISCO}})$$( r ISCO ) and the efficiency $$(\eta )$$( η ) of the accretion disk in converting matter into radiation. We employ a simplified model to describe the disk’s radiative flux, and differential and spectral luminosity. Subsequently, we compare our findings with the expectations from accretion disks around Kerr black holes. Notably, our calculations reveal that both the luminosity of the accretion disk and its efficiency are greater when considering the geometry of rotating regular black holes, particularly for fixed and small values of the spin parameter (j), in contrast to the predictions obtained using the Kerr metric for a black hole of the same mass. These results offer intriguing insights into the behavior of astrophysical black holes.

We check the dynamical and observational features of four typologies of logotropic dark energy models, leading to a thermodynamic cosmic speed up fueled by a single fluid that unifies dark energy and dark matter. We first present two principal Anton-Schmidt fluids where the Grüneisen parameter ${\gamma }_{\mathrm{G}}$ is free to vary and then fixed to the special value ${\gamma }_{\mathrm{G}}=\frac{5}{6}$. We also investigate the pure logotropic model, corresponding to ${\gamma }_{\mathrm{G}}=-\frac{1}{6}$. Finally, we propose a new logotropic paradigm that works as a generalized logotropic fluid, in which we split the role of dark matter and baryons. We demonstrate that the logotropic paradigms may present drawbacks in perturbations, showing a negative adiabatic sound speed which make perturbations unstable. We thus underline which model is favored over the rest. The Anton-Schmidt model with ${\gamma }_{\mathrm{G}}=\frac{5}{6}$ is ruled out while the generalized logotropic fluid seems to be the most suitable one, albeit weakly disfavored than the $\mathrm{\Lambda }\mathrm{CDM}$ model. To fix numerical constraints, we combine low- and higher-redshift domains through experimental fits based on Monte Carlo Markov Chain procedures, taking into account the most recent Pantheon supernovae Ia catalog, Hubble measurements, and ${\sigma }_8$ data points based on the linear growth function for the large scale structures. We also consider two model selection criteria to infer the statistical significance of the four models under examination. We conclude there is a statistical advantage to handle the Anton-Schmidt fluid with the Grüneisen parameter free to vary and/or fixed to ${\gamma }_{\mathrm{G}}=-\frac{1}{6}$. The generalized logotropic fluid indicates suitable results, more statistically favored than the other models until the sound speed is positive, becoming unstable in perturbations elsewhere. We emphasize that the $\mathrm{\Lambda }\mathrm{CDM}$ paradigm works statistically better than any kind of logotropic and generalized logotropic models, while the Chevallier-Polarski-Linder parametrization is statistically comparable with logotropic scenarios. Finally, we propose that generalizing the Grüneisen parameter by including the effects of temperature would guarantee the sound speed to be positive definite at all redshifts.