Black Holes in Bulk Viscous Cosmology

We investigate the effects of the accretion of phantom energy with non-zero bulk viscosity onto a Schwarzschild black hole and show that black holes accreting viscous phantom energy will lose mass rapidly compared to the non-viscous case. When matter is incorporated along with the phantom energy, the black holes meet with the same fate as bulk viscous forces dominate matter accretion. If the phantom energy has large bulk viscosity, then the mass of the black hole will reduce faster than in the small viscosity case.     

Fate of an accretion disc around a black hole when both the viscosity and dark energy is in effect

This paper deals with the viscous accretion flow of a modified Chaplygin gas towards a black hole as the central gravitating object. A modified Chaplygin gas is a particular type of dark energy model which mimics of radiation era to phantom era depending on the different values of its parameters. We compare the dark energy accretion with the flow of adiabatic gas. An accretion disc flowing around a black hole is an example of a transonic flow. To construct the model, we consider three components of the Navier–Stokes equation, the equation of continuity and the modified Chaplygin gas equation of state. As a transonic flow passes through the sonic point, the velocity gradient being apparently singular there, it gives rise to two flow branches: one in-falling, the accretion and the other outgoing, the wind. We show that the wind curve is stronger and the wind speed reaches that of light at a finite distance from the black hole when dark energy is considered. Besides, if we increase the viscosity, the accretion disc is shortened in radius. These two processes acting together make the system deviate much from the adiabatic accretion case. It shows a weakening process for the accretion procedure by the work of the viscous system influencing both the angular momentum transport and the repulsive force of the modified Chaplygin gas.     

Convection-Dominated Accretion Flows with Radiative Cooling

By numerically solving the set of basic equations describing black hole accretion flows with low accretion rates, we show that although the dynamical structure of these flows is essentially unaffected by radiative processes in comparison with the case in which the radiation is not considered, the radiative cooling can be more important than the advective cooling in the flow＇s convection-dominated zone, and this result may have implications to distinguish observationally convection-dominated accretion flows from advection-dominated accretion flows.     

Effects of viscosity on shock-induced damping of an initial sinusoidal disturbance

A lack of reliable data treatment method has been for several decades the bottleneck of viscosity measurement by disturbance amplitude damping method of shock waves.In this work the finite difference method is firstly applied to obtain the numerical solutions for disturbance amplitude damping behavior of sinusoidal shock front in inviscid and viscous flow.When water shocked to 15 GPa is taken as an example,the main results are as follows:(1) For inviscid and lower viscous flows the numerical method gives results in good agreement with the analytic solutions under the condition of small disturbance(a0/λ=0.02);(2) For the flow of viscosity beyond 200 Pa s(η=κ) the analytic solution is found to overestimate obviously the effects of viscosity.It is attributed to the unreal pre-conditions of analytic solution by Miller and Ahrens;(3) The present numerical method provides an effective tool with more confidence to overcome the bottleneck of data treatment when the effects of higher viscosity in experiments of Sakharov and flyer impact are expected to be analyzed,because it can in principle simulate the development of shock waves in flows with larger disturbance amplitude,higher viscosity,and complicated initial flow.     

Viscous shear in general-relativistic astrophysical flows

Conclusion Introducing the concept of general co-moving frames (gcmf) in [4] we have argued that it may become useful in a number of hydrodynamical and mhd applications. In [5] using thegcmf technique we have constructed a fully covariant, general-relativistic theory of strongly magnetized collisionless plasma. The approach proved itself to be highly convenient-it allowed us to find new equations of state for such a medium.In the present paper we have considered viscous shear in generalrelativistic astrophysical flows as an another example of the effective usage of orthonormal tetrads method. Namely, we have specified general corotating frames (gcrf)-subclass ofgcmf corresponding to the flows being in purely rotational motion. By means of gcrf we have been able to find expressions for nonzero components of shear tensor and turbulent viscosity tensor for the innermost region of a black hole accretion disc.We think that the method may be useful when considering analogous problems with astrophysical flows of more complicated geometry and/or dynamics. In particular, the method may become efficient for jets in active galactic nuclei (agn) and quasars [13], general-relativistic winds of compact objects [14] and the innermost regions of candidates for galactic black hole accretion discs [15]. To be sure, in some of these problems we have to use a more general set ofgcmf instead ofgcrf. Such problems, however, are beyond the scope of this paper, where we have only outlined the main background of the method and demonstrated its productivity in a simple case of quasi-keplerian accretion flow in a general-relativistic standard accretion disc.     

A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows

In this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for simulation of viscous compressible flows. In the solver, the finite volume method is applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes solvers, in this work, the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model, while the viscous flux is still approximated by conventional smooth function approximation. The present work overcomes the two major drawbacks of existing LBFS [28–31], which is used for simulation of inviscid flows. The first one is its ability to simulate viscous flows by including evaluation of viscous flux. The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux, which takes a value close to zero in the boundary layer and one around the strong shock wave. Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.     

Constraints on Slim Accretion Discs

We show that when the gravitational force in the vertical direction is correctly calculated, the well-known S- shaped sequence of thermal equilibrium solutions can be constructed only for small radii of black hole accretion flows, such that slim accretion discs can possibly exist only in the inner regions of these flows.     

A Switch Function-Based Gas-Kinetic Scheme for Simulation of Inviscid and Viscous Compressible Flows

In this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presented for the simulation of inviscid and viscous compressible flows. With the finite volume discretization, Euler and Navier-Stokes equations are solved and the SF-GKS is applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained by the conventional smooth function approximation. Unlike the traditional gas-kinetic scheme in the calculation of inviscid flux such as Kinetic Flux Vector Splitting (KFVS), the numerical dissipation is controlled with a switch function in the present scheme. That is, the numerical dissipation is only introduced in the region around strong shock waves. As a consequence, the present SF-GKS can well capture strong shock waves and thin boundary layers simultaneously. The present SF-GKS is firstly validated by its application to the inviscid flow problems, including 1-D Euler shock tube, regular shock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscous transonic and hypersonic flow problems. Good agreement between the present results and those in the literature verifies the accuracy and robustness of SF-GKS.     

Equilibrium of a gravitating plasma in a dipolar magnetic field

The equilibria of plasma in a dipolar magnetic field under the gravitational influence of a massive body (a star or black hole) and a self gravitating plasma are considered. Analytical solutions are found that can be useful for understanding the physics of plasma flows in accretion disks and star formation.     

Behavior of viscous solutions in Lagrangian formulation

In this paper, the behavior of shock-capturing methods in Lagrangian coordinate is investigated. The relation between viscous shock and inviscid one is analyzed quantitatively, and the procedure of a viscous shock formation and propagation with a jump type initial data is described. In general, a viscous shock profile and a discontinuous one include different energy and momentum, and these discrepancies result in the generation of waves in all families when a single wave Riemann problem (shock or rarefaction) is solved. Employing this method, some anomalous behavior, such as, viscous shock interaction, shock passing through ununiform grids, postshock oscillations and lower density phenomenon is explained well. Using some classical schemes to solve the inviscid flow in Lagrangian coordinate may be not adequate enough to correctly describe flow motion in the discretized space. Partial discrepancies between von Neumann artificial viscosity method and Godunov method are exhibited. Some reviews are given to those methods which can ameliorate even eliminate entropy errors. A hybrid scheme based on the understanding to the behavior of viscous solution is proposed to suppress the overheating error.     

Evolution of a Schwarzschild black hole in phantom-like Chaplygin gas cosmologies

In the classical relativistic regime, the accretion of phantom energy onto a black hole reduces the mass of the black hole. In this context, we have investigated the evolution of a Schwarzschild black hole in the standard model of cosmology using the phantom-like modified variable Chaplygin gas and the viscous generalized Chaplygin gas. The corresponding expressions for accretion time scale and evolution of mass have been derived. Our results indicate that the mass of the black hole will decrease if the accreting phantom Chaplygin gas violates the dominant energy condition and will increase in the opposite case. Thus, our results are in agreement with the results of Babichev et al. who first proposed this scenario.     

Stability of Viscous Shocks in Isentropic Gas Dynamics

In this paper, we examine the stability problem for viscous shock solutions of the isentropic compressible Navier–Stokes equations, or p-system with real viscosity. We first revisit the work of Matsumura and Nishihara, extending the known parameter regime for which small-amplitude viscous shocks are provably spectrally stable by an optimized version of their original argument. Next, using a novel spectral energy estimate, we show that there are no purely real unstable eigenvalues for any shock strength. By related estimates, we show that unstable eigenvalues are confined to a bounded region independent of shock strength. Then through an extensive numerical Evans function study, we show that there are no unstable spectra in the entire right-half plane, thus demonstrating numerically that large-amplitude shocks are spectrally stable up to Mach number M ≈ 3000 for 1 ≤ γ ≤ 3. This strongly suggests that shocks are stable independent of amplitude and the adiabatic constant γ. We complete our study by showing that finite-difference simulations of perturbed large-amplitude shocks converge to a translate of the original shock wave, as expected. This work was supported in part by the National Science Foundation award numbers DMS-0607721 and DMS-0300487.     

Extension of the finite volume particle method to viscous flow

The finite volume particle method (FVPM) is a mesh-free method for fluid dynamics which allows simple and accurate implementation of boundary conditions and retains the conservation and consistency properties of classical finite volume methods. In this article, the FVPM is extended to viscous flows using a consistency-corrected smoothed particle hydrodynamics (SPH) approximation to evaluate velocity gradients. The accuracy of the viscous FVPM is improved by a higher-order discretisation of the inviscid flux combined with a second-order temporal discretisation. The higher-order inviscid FVPM is validated for a 1-D shock tube problem, in which it demonstrates an enhanced shock capturing ability. For two-dimensional simulations, a small arbitrary Lagrange–Euler correction to fully Lagrangian particle motion is beneficial in maintaining a favourable particle distribution over long simulation times. The viscous FVPM is validated for two-dimensional Poiseuille, Taylor–Green and lid-driven cavity flows, and good agreement is achieved with analytic or reference numerical solutions. These results establish the viability of FVPM as a tool for mesh-free simulation of viscous flows in engineering.     

Black hole binaries and microquasars

This is a general review Oil the observations and physics of black hole X-ray binaries and microquasars, with the emphasize on recent developments in the high energy regime. The focus is put on understanding the accretion flows and measuring the parameters of black holes in them. It includes mainly two parts： i） Brief review of several recent review article on this subject; ii） Further development on several topics, including black hole spin measurements, hot accretion flows, corona formation, state transitions and thermal stability of standard think disk. This is thus not a regular bottom-up approach, which I feel not necessary at this stage. Major effort is made in making and incorporating from many sources useful plots and illustrations, in order to make this article more comprehensible to non-expert readers. In the end I attempt to make a unification scheme on the accretion-outflow （wind/jet） connections of all types of aecreting BHs of all accretion rates and all BH mass scales, and finally provide a brief outlook.     

Front Speed in the Burgers Equation with a Random Flux

We study the large-time asymptotic shock-front speed in an inviscid Burgers equation with a spatially random flux function. This equation is a prototype for a class of scalar conservation laws with spatial random coefficients such as the well-known Buckley–Leverett equation for two-phase flows, and the contaminant transport equation in groundwater flows. The initial condition is a shock located at the origin (the indicator function of the negative real line). We first regularize the equation by a special random viscous term so that the resulting equation can be solved explicitly by a Cole–Hopf formula. Using the invariance principle of the underlying random processes and the Laplace method, we prove that for large times the solutions behave like fronts moving at averaged constant speeds in the sense of distribution. However, the front locations are random, and we show explicitly the probability of observing the head or tail of the fronts. Finally, we pass to the inviscid limit, and establish the same results for the inviscid shock fronts.     

Numerical modelling of free interaction of shock waves in corner flows

The inviscid supersonic flows in corners between intersecting compression wedges were studied numerically. Under usual conditions, the flows in such corner configurations are conically self-similar. Besides, shock waves formed by wedges are plane and they interact with one another in these flows and the downstream development of the shock interaction structure at that occurs in a region which is bounded in cross-sectional directions by the walls and contracts towards the corner rib, and in this sense the above interaction of shocks may be subjected to influence of the rib. The corner flows of another type with an interaction of shocks not subjected to the “rib effect”, in other words free, were considered. This was ensured by that the corner configurations were designed with a gradually expanding gap along the rib in a way that the reflected shocks arising as a result of interaction passed through the gap without falling onto the walls. This eliminated the influence of a local flow near the corner rib on the interaction of plane shock waves formed by the wedges. The inviscid flows symmetric with respect to the bisector plane of the corner dihedral angle were considered. The computations showed that, in the gapped corner configurations with the free interaction of shocks, if these interactions were irregular, the cross-flow patterns were practically the same as in the original corner configurations without a gap. The conditions for the flows over corner configurations were also considered under which the interaction of shocks corresponded to the Neumann criterion of mechanical equilibrium. These conditions are equivalent to those, which take place in two-dimensional steady flows, when a hysteresis phenomenon is possible, which manifests itself in changing the moment of transition from a regime of regular reflection of shocks to an irregular one and conversely at a direct and inverse courses of varying the flow parameters—the Mach number and the inclination angle of the wedges. The conducted computations showed that a hysteresis is possible for considered corner flows in gapped configurations, but it must be followed by a detachment of shocks from the corner apex and a breakdown of the conical flow structure.     

Accretion on high derivative asymptotically safe black holes

Asymptotically safe gravity is an effective approach to quantum gravity.It is important to differentiate modified gravity,which is inspired by asymptotically safe gravity.In this study,we examine particle dynamics near the improved version of a Schwarzschild black hole.We assume that in the context of an asymptotically safe gravity scenario,the ambient matter surrounding the black hole is of isothermal nature,and we investigate the spherical accretion of matter by deriving solutions at critical points.The analysis of various values of the state parameter for isothermal test fluids,viz.,k=1,1/2,1/3,1/4 show the possibility of accretion onto an asymptotically safe black hole.We formulate the accretion problem as Hamiltonian dynamical system and explain its phase flow in detail,which reveals interesting results in the asymptotically safe gravity theory.     

Shadow images and observed luminosity of the Bardeen black hole surrounded by different accretions

In this paper, by exploring photon motion in the region near a Bardeen black hole, we studied the shadow and observed properties of the black hole surrounded by various accretion models. We analyzed the changes in shadow imaging and observed luminosity when the relevant physical parameters are changed. For the different spherical accretion backgrounds, we find that the radius of shadow and the position of the photon sphere do not change, but the observed intensity of shadow in the infalling accretion model is significantly lower than that in the static case. We also studied the contribution of the photon rings, lensing rings and direct emission to the total observed flux when the black hole is surrounded by an optically thin disk accretion. Under the different forms of the emission modes, the results show that the observed brightness is mainly determined by direct emission, while the lensing rings will provide a small part of the observed flux, and the flux provided by the photon ring is negligible. By comparing our results with the Schwarzschild spacetime, we find that the existence or change of relevant status parameters will greatly affect the shape and observed intensity of the black hole shadow. These results support the theory that the change of state parameter will affect the spacetime structure, thus affecting the observed features of black hole shadows.     

The shadow and observation appearance of black hole surrounded by the dust field in Rastall theory

In the context of Rastall gravity, the shadow and observation intensity casted by the new Kiselev-like black hole with dust field have been numerically investigated. In this system, the Rastall parameter and surrounding dust field structure parameter have considerable consequences on the geometric structure of spacetime. Considering the photon trajectories near the black hole, we investigate the variation of the radii of photon sphere, event horizon and black hole shadow under the different related parameters. Furthermore, taking into account two different spherically symmetric accretion models as the only background light source, we also studied the observed luminosity and intensity of black holes. For the both spherical accretions background, the results show that the decrease or increase of the observed luminosity depends on the value range of relevant parameters, and the promotion effect is far less obvious than the attenuation effect on the observed intensity. One can find that the inner shadow region and outer bright region of the black hole wrapped by infalling accretion are significantly darker than those of the static model, which is closely related to the Doppler effect. In addition, the size of the shadow and the position of the photon sphere are always the same in the two accretion models, which means that the black hole shadow depend only on the geometry of spacetime, while the observation luminosity is affected by the form of accretion material and the related spacetime structure.     

Implications of a viscosity bound on black hole accretion

Motivated by the viscosity bound in gauge/gravity duality, we consider the ratio of shear viscosity (η) to entropy density (s  ) in black hole accretion flows. We use both an ideal gas equation of state and the QCD equation of state obtained from lattice for the fluid accreting onto a Kerr black hole. The QCD equation of state is considered since the temperature of accreting matter is expected to approach ¹⁰¹² K${10}^{12}\text{K}$ in certain hot flows. We find that in both the cases η/s$\eta /s$ is small only for primordial black holes and several orders of magnitude larger than any known fluid for stellar and supermassive black holes. We show that a lower bound on the mass of primordial black holes leads to a lower bound on η/s$\eta /s$ and vice versa. Finally we speculate that the Shakura–Sunyaev viscosity parameter should decrease with increasing density and/or temperatures.