We investigate the motion of test particles in the gravitational field of a static naked singularity generated by a mass distribution with a quadrupole moment. We use the quadrupole metric ($q$ metric) which is the simplest generalization of the Schwarzschild metric with a quadrupole parameter. We study the influence of the quadrupole on the motion of massive test particles and photons and show that the behavior of the geodesics can drastically depend on the values of the quadrupole parameter. In particular, we prove explicitly that the perihelion distance depends on the value of the quadrupole. Moreover, we show that an accretion disk on the equatorial plane of the quadrupole source can be either continuous or discrete, depending on the value of the quadrupole. The inner radius of the disk can be used in certain cases to determine the value of the quadrupole parameter. The case of a discrete accretion is interpreted as due to the presence of repulsive gravity generated by the naked singularity. Radial geodesics are also investigated and compared with the Schwarzschild counterparts.

We consider the observational properties of a static black hole space–time immersed in a dark matter envelope. We investigate how the modifications to geometry induced by the presence of dark matter affect the luminosity of the black hole’s accretion disc. We show that the same disc luminosity as produced by a black hole in vacuum may be produced by a smaller black hole surrounded by dark matter under certain conditions. In particular, we demonstrate that the luminosity of the disc is markedly altered by the presence of dark matter, suggesting that the mass estimation of distant supermassive black holes may be changed if they are immersed in dark matter. We argue that a similar effect holds in more realistic scenarios, and we discuss the refractive index related to dark matter lensing. Finally, we show how the results presented here may help to explain the observed luminosity of supermassive black holes in the early Universe.

Observations of gamma-ray bursts up to z ∼ 9 are best suited to study the possible evolution of the universe equation of state at intermediate redshifts. We apply the Combo relation to a sample of 174 gamma-ray bursts to investigate possible evidence of evolving dark energy parameter w(z). We first build a gamma-ray burst Hubble’s diagram and then we estimate the set (Ω _m , Ω_Λ) in the framework of flat and non-flat ΛCDM paradigm. We then get bounds over the wCDM model, where w is thought to evolve with redshift, adopting two priors over the Hubble constant in tension at 4.4σ, i.e., H ₀ = (67.4 ± 0.5) km s⁻¹ Mpc⁻¹ and H ₀ = (74.03 ± 1.42) km s⁻¹ Mpc⁻¹. We show our new sample provides tighter constraints on Ω _m since at z ≤ 1.2 we see that w(z) agrees within 1σ with the standard value w = −1. The situation is the opposite at larger z, where gamma-ray bursts better fix w(z) that seems to deviate from w = −1 at 2σ and 4σ level, depending on the redshift bins. In particular, we investigate the w(z) evolution through a piecewise formulation over seven redshift intervals. From our fitting procedure we show that at z ≥ 1.2 the case w < −1 cannot be fully excluded, indicating that dark energy’s influence is not negligible at larger z. We confirm the Combo relation as a powerful tool to investigate cosmological evolution of dark energy. Future space missions will significantly enrich the gamma-ray burst database even at smaller redshifts, improving de facto the results discussed in this paper.

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 study extended classes of logotropic fluids as unified dark energy models. Under the hypothesis of the Anton–Schmidt scenario, we consider a universe obeying a single fluid model with a...