The numerical investigation of the Bondi-Hoyle accretion on to a moving black hole has a long history, both in Newtonian and in general-relativistic physics. By performing new twodimensional and general-relativistic simulations on to a rotating black hole, we point out a novel feature, namely that quasi-periodic oscillations (QPOs) are naturally produced in the shock cone that develops in the downstream part of the flow. Because the shock cone in the downstream part of the flow acts as a cavity trapping pressure perturbations, modes with frequencies in the integer ratios of 2:1 and 3:1 are easily produced. The frequencies of these modes depend on the black hole spin and on the properties of the flow, and scale linearly with the inverse of the black hole mass. Our results may be relevant for explaining the detection of QPOs in Sagittarius A * , once such detection is confirmed by further observations. Finally, we report on the development of the flip-flop instability, which can affect the shock cone under suitable conditions; such an instability has been discussed before in Newtonian simulations but was never found in a relativistic regime.

In this paper, the general procedure to solve the General Relativistic Hydrodynamical(GRH) equations with Adaptive-Mesh Refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of general relativistic hydrodynamic equations are done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second order convergence of the code in 1D, 2D and 3D. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the general relativistic hydrodynamical equations are tested using two different test problems which are Geodesic flow and Circular motion of particle In order to this, the flux part of GRH equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time.

We present the numerical study of dynamical instability of a pressure-supported relativistic torus, rotating around the black hole with a constant specific angular momentum on a fixed space-time background, in case of perturbation by a matter coming from the outer boundary. Two dimensional hydrodynamical equations are solved at equatorial plane using the HRSCS to study the effect of perturbation on the stable systems. We have found that the perturbed torus creates an instability which causes the gas falling into the black hole in a certain dynamical time. All the models indicate an oscillating torus with certain frequency around their instant equilibrium. The dynamic of the accreted torus varies with the size of initial stable torus, black hole spin and other variables, such as Mach number, sound speed, cusp location of the torus, etc. The mass accretion rate is slightly proportional to the torus-to-hole mass ratio in the black hole-torus system, but it strongly depends on the cusp location of the torus. The cusp located in the equipotential surfaces of the effective potential moves outwards into the torus. The dynamical change of the torus increases the mass accretion rate and triggers the Papaloizou-Pringle instability. It is also observed that the growth of the m = 1 mode of the Papaloizou-Pringle instability occurs for a wide range of fluid and hydrodynamical parameters and a black hole spin. We have also computed the QPOs from the oscillating relativistic torus.

In this paper, the numerical investigation of a Bondi–Hoyle accretion around a non-rotating black hole in a novel four dimensional Einstein–Gauss–Bonnet gravity is investigated by solving the general relativistic hydrodynamical equations using the high resolution shock capturing scheme. For this purpose, the accreated matter from the wind-accreating X-ray binaries falls towards the black hole from the far upstream side of the domain, supersonically. We study the effects of Gauss–Bonnet coupling constant $$\alpha $$ α in 4D EGB gravity on the accreated matter and shock cones created in the downstream region in detail. The required time having the shock cone in downstream region is getting smaller for $$\alpha > 0$$ α > 0 while it is increasing for $$\alpha < 0$$ α < 0 . It is found that increases in $$\alpha $$ α leads violent oscillations inside the shock cone and increases the accretion efficiency. The violent oscillations would cause increase in the energy flux, temperature, and spectrum of X-rays. So the quasi-periodic oscillations (QPOs) are naturally produced inside the shock cone when $$-5 \le \alpha \le 0.8$$ - 5 ≤ α ≤ 0.8 . It is also confirmed that EGB black hole solution converges to the Schwarzschild one in general relativity when $$\alpha \rightarrow 0$$ α → 0 . Besides, the negative coupling constants also give reasonable physical solutions and increase of $$\alpha $$ α in negative directions suppresses the possible oscillation observed in the shock cone.

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It is known from recent numerical calculations that Bondi-Hoyle accretion creates a shock cone behind compact objects. This type of accretion leads to instabilities, which can explain certain astrophysical phenomena. In this paper, our main goal is to find the flip-flop behaviour of the shock cone in the relativistic region. In order to do so we have modelled the dynamics of a shock cone around non-rotating and rotating black holes at the equatorial plane in 2D. The effects of the various parameters on the shock cones and instabilities, such as the asymptotic velocity, sound speed, Mach number and adiabatic index, are studied. We have determined the mass accretion rate, shock opening angle, shock cone oscillation, quasi-periodic oscillations (QPOs), and growth rate of instabilities to reveal the disc properties and its radiation. We have discovered, for the first time, flip-flop instabilities around a black hole in the relativistic region by solving the general relativistic hydrodynamical equations. The flip-flop instabilities are found for sound speeds C s,∞ < 0.2 with moderate Mach numbers (∼M = 3 and M = 4 for C s,∞ = 0.1 or M = 7 and M = 8 for C s,∞ = 0.05). Our calculation clearly confirms that the shock cone should be detached from the black hole in the Bondi-Hoyle accretion flow with ≥ 2 for non-rotating and rotating black holes. Results reveal that the flip-flopping shock cone not only creates a torque effect on the black hole but also produces continuous X-ray flares with a certain frequency. Furthermore, QPOs originate inside the shock cone and are stronger in regions that have a radius of a few gravitational radii away from the centre owing to the flip-flop oscillation. Finally, our results are compared with the results of numerical and theoretical calculations in Newtonian hydrodynamics, and it is found that they are in good agreement.

A numerical study of the dynamic of the nonselfgravitating, unmagnetized, nonaxisymmetric, and rotating the torus around the non-rotating black hole is presented. We investigate the instability of the rotating torus subject to perturbations presented by increasing or decreasing the angular velocity of the stable torus. We have done, for the first time, an extensive analysis of the torus dynamic response to the perturbation of the angular velocity of the stable torus. We show how the high, moderate, and low values of the perturbations affect the torus dynamic and help us to understand the properties of the instability and Quasi-Periodic Oscillation (QPO). Our numerical simulations indicate the presence of Papaloizou-Pringle instability (PPI) with global m = 1 mode and QPOs for the moderate and lower values of the perturbations on the angular velocity of the stable torus. Furthermore, with the lower values of the perturbations, the torus can lead to a wiggling initially and then PPI is produced in it. Finally, the matter of the torus would be dissipated due to the presence of a strong torque.

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∞ (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 α. 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.