To explain the observed X-ray data in a black hole–accreting matter system and understand the physical mechanisms behind QPOs, we have numerically modeled the dynamical and oscillation properties of the shock cone formed around both slowly and rapidly rotating Hartle–Thorne black holes, resulting from the mechanism of Bondi–Hoyle–Lyttleton (BHL). According to the numerical simulations, an increase in the quadrupole parameter leads to a decrease in the shock cone opening angle around the black hole. A larger quadrupole parameter results in more matter falling into the black hole within the cone. The combination of the quadrupole parameter and black hole rotation causes the matter inside the cone to exhibit chaotic motion. These dynamical changes and chaotic behavior of the shock cones excite the fundamental oscillation modes. Moreover, new frequencies have been formed due to the nonlinear coupling of the fundamental modes. Conversely, we have numerically studied the behavior of cones formed around rapidly rotating Hartle–Thorne black holes and found differences and similarities to those obtained from slowly rotating cases. Finally, comparing the outcomes obtained fromHartle–Thorne gravity with the results fromKerr and Einstein–Gauss–Bonnet (EGB) gravities reveals the impact of the quadrupole parameter on the shock cone and QPOs.

Understanding the physical structures of the accreted matter very close to a black hole in quasars and active galactic nucleus (AGN) is an important milestone to constrain the activities occurring in their centers. In this paper, we numerically investigate the effects of the asymptotic velocities on the physical structures of the accretion disk around the Kerr and Einstein–Gauss–Bonnet (EGB) rapidly rotating black holes. The Bondi–Hoyle accretion is considered with a falling gas towards the black hole in an upstream region of the computational domain. Shock cones are naturally formed in the downstream part of the flow around both black holes. The structure of the cones and the amount of the accreted matter depend on asymptotic velocity $V_{\infty }$ (Mach number) and the types of the gravities (Kerr or EGB). Increasing the Mach number of the in-flowing matter in the supersonic region reduces the shock opening angle and the accretion rates, because of the gas rapidly falling towards the black hole. The EGB gravity leads to an increase in the shock opening angle of the shock cones while the mass-accretion rates $dM/dt$ decrease in EGB gravity with a Gauss–Bonnet (GB) coupling constant $\alpha$. It is also confirmed that accretion rates and drag forces are significantly altered in the EGB gravity. Our numerical simulation results could be used in identifying the accretion mechanism and physical properties of the accretion disk and black hole in the observed X-rays such as NGC 1313 X-1 and 1313 X-2 and MAXI J1803-298.

An inelastic pulsed neutron scattering study was performed on the dependence of the dispersion and spectral intensity of the in-plane Cu-O bond-stretching LO phonon mode on doped charge density. The measurements were made in the time-of-flight mode with the multiangle position sensitive spectrometer of the ISIS facility on single crystals of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ ($x=0.15$, 0.35, 0.6, 0.7, and 0.95). The focus of the study is the in-plane Cu-O bond-stretching LO phonon mode, which is known for strong electron-phonon coupling and unusual dependence on composition and temperature. It is shown that the dispersions for the samples with $x=0.35$, 0.6, and 0.7 are similar to the superposition of those for $x=0.15$ and 0.95 samples, and cannot be explained in terms of the structural anisotropy. It is suggested that the results are consistent with the model of nanoscale electronic phase separation, with the fraction of the phases being dependent on the doped charge density.

The Dynamic Hubbard Model (DHM) has been introduced as a framework for the electron-hole asymmetry observed in materials like high-temperature superconductors. In this study, we aim to understand the intricate dynamics of hole interactions, particularly focusing on the competition between on-site repulsion and hole-lattice coupling. Our results reveal a striking feature-an effective nearest-neighbor attraction between holes, even in the presence of the on-site repulsion typical of Mott insulators. Notably, the on-site repulsion not only coexists but also enhances the nearest-neighbor coupling. Our exploration of the DHM unravels unexpected and significant characteristics, enriching our understanding of hole interactions in correlated electron systems. The model’s capacity to capture both on-site repulsion and effective nearest-neighbor attraction offers a valuable perspective.