Patryk Mach

Universality and backreaction in a general-relativistic accretion of steady fluids

The spherically symmetric steady accretion of polytropic perfect fluids onto a black hole is the simplest flow model that can demonstrate the effects of backreaction. The analytic and numerical investigation reveals that backreaction keeps intact most of the characteristics of the sonic point. For any such system, with the free parameter being the relative abundance of the fluid, the mass accretion rate achieves maximal value when the mass of the fluid is 1/3 of the total mass. Fixing the total mass of the system, one observes the existence of two weakly accreting regimes, one overabundant and the other poor in fluid content.

Stability of relativistic Bondi accretion in Schwarzschild-(anti-)de Sitter spacetimes

In a recent paper we investigated stationary, relativistic Bondi-type accretion in Schwarzschild-(anti-)de Sitter spacetimes. Here we study their stability, using the method developed by Moncrief. The analysis applies to perturbations satisfying the potential flow condition. We prove that global isothermal flows in Schwarzschild-anti-de Sitter spacetimes are stable, assuming the test-fluid approximation. Isothermal flows in Schwarzschild-de Sitter geometries and polytropic flows in Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter spacetimes can be stable, under suitable boundary conditions.

Stability of self-gravitating accreting flows

Analytic methods show stability of the stationary accretion of test fluids but they are inconclusive in the case of self-gravitating stationary flows. We investigate numerically stability of those stationary flows onto compact objects that are trans-sonic and rich in gas. In all studied examples solutions appear stable. Numerical investigation suggests also that the analogy between sonic and event horizons holds for small perturbations of compact support but fails in the case of finite perturbations.

All solutions of the n = 5 Lane–Emden equation

All real solutions of the Lane–Emden equation for n = 5 are obtained in terms of Jacobian and Weierstrass elliptic functions. A new family of solutions is found. It is expressed by remarkably simple formulae involving Jacobian elliptic functions only. The general properties and discrete scaling symmetries of these new solutions are discussed. We also comment on their possible applications.

On the stability of steady general-relativistic accretion and analogue black holes

Investigation of general-relativistic spherically symmetric steady accretion of self-gravitating perfect fluid onto compact objects reveals the existence of two weakly accreting regimes. In the first (corresponding to the test fluid approximation), the mass of the central object is much larger than the mass of the accreting fluid; in the second, the mass of the fluid dominates. The stability of the solutions belonging to the first regime has been proved by Moncrief. In this work we report the results of a series of numerical studies demonstrating stability of massive solutions, i.e. belonging to the second of the aforementioned regimes. It is also shown that a formal analogy between “sonic horizons” in the accretion picture and event horizons in general relativity is rather limited. The notion of a “sonic horizon” is only valid in a linear regime of small hydrodynamical perturbations. Strong perturbations can still escape from beneath the ”sonic horizon.“

General-relativistic versus Newtonian: Geometric dragging and dynamic antidragging in stationary self-gravitating disks in the first post-Newtonian approximation

We evaluate general-relativistic effects in motion of stationary accretion disks around a Schwarzschild black hole, assuming the first post-Newtonian (1PN) approximation. There arises an integrability condition, that leads to the emergence of two types of general-relativistic corrections to a Newtonian rotation curve. The well known geometric dragging of frames accelerates rotation but the hitherto unknown dynamic term, that reflects the disk structure, deccelerates rotation. The net result can diminish the Newtonian angular velocity of rotation in a central disk zone but the geometric dragging of frames dominates in the disk boundary zone. Both effects are nonlinear in nature and they disappear in the limit of test fluids. Dust disks can be only geometrically dragged while uniformly rotating gaseous disk are untouched at the 1PN order. General-relativistic contributions can strongly affect rotation periods in Keplerian motion for compact systems.

Homoclinic accretion solutions in the Schwarzschild–anti–de Sitter space-time

The aim of this paper is to clarify the distinction between homoclinic and standard (global) Bondi-type accretion solutions in the Schwarzschild-anti-de Sitter spacetime. The homoclinic solutions have recently been discovered numerically for polytropic equations of state. Here I show that they exist also for certain isothermal (linear) equations of state, and an analytic solution of this type is obtained. It is argued that the existence of such solutions is generic, although for sufficiently relativistic matter models (photon gas, ultra-hard equation of state) there exist global solutions that can be continued to infinity, similarly to standard Michels solutions in the Schwarzschild spacetime. In contrast to that global solutions should not exist for matter models with a non-vanishing rest-mass component, and this is demonstrated for polytropes. For homoclinic isothermal solutions I derive an upper bound on the mass of the black hole for which stationary transonic accretion is allowed.

SELFGRAVITATION IN A GENERAL-RELATIVISTIC ACCRETION OF STEADY FLUIDS

The selfgravity of an infalling gas can alter significantly the accretion of gases. In the case of spherically symmetric steady flows of polytropic perfect fluids the mass accretion rate achieves maximal value when the mass of the fluid is 1/3 of the total mass. There are two weakly accreting regimes, one over-abundant and the other poor in fluid content. The analysis within the newtonian gravity suggests that selfgravitating fluids can be unstable, in contrast to the accretion of test fluids.

Michel accretion of a polytropic fluid with adiabatic index : global flows versus homoclinic orbits

We analyze the properties of a polytropic fluid that is radially accreted into a Schwarzschild black hole. The case where the adiabatic index γ lies in the range of has been treated in previous work. In this article, we analyze the complementary range of . To this purpose, the problem is cast into an appropriate Hamiltonian dynamical system, whose phase flow is analyzed. While, for , the solutions are always characterized by the presence of a unique critical saddle point, we show that, when , an additional critical point might appear, which is a center point. For the parametrization used in this paper, we prove that, whenever this additional critical point appears, there is a homoclinic orbit. Solutions corresponding to homoclinic orbits differ from standard transonic solutions with vanishing asymptotic velocities in two aspects: they are local (i.e., they cannot be continued to arbitrarily large radii); the dependence of the density or the value of the velocity on the radius is not monotonic.

Exact solution of the hydrodynamical Riemann problem with nonzero tangential velocities and the ultrarelativistic equation of state.

We give a solution of the Riemann problem in relativistic hydrodynamics in the case of ultrarelativistic equation of state and nonvanishing components of the velocity tangent to the initial discontinuity. Simplicity of the ultrarelativistic equation of state (the pressure being directly proportional to the energy density) allows us to express this solution in analytical terms. The result can be used both to construct and test numerical schemes for relativistic Euler equations in (3+1) dimensions.