The Shock Cone Instabilities and Quasi-Periodic Oscillations around the Hartle-Thorne Black Hole

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.