Axisymmetric black hole accretion in the Kerr metric as an autonomous dynamical system

Abstract

In a stationary, general relativistic, axisymmetric, inviscid and rotational accretion flow, described within the Kerr geometric framework, transonicity has been examined by setting up the governing equations of the flow as a first-order autonomous dynamical system. The consequent linearised analysis of the critical points of the flow leads to a comprehensive mathematical prescription for classifying these points, showing that the only possibilities are saddle points and centre-type points for all ranges of values of the fixed flow parameters. The spin parameter of the black hole influences the multitransonic character of the flow, as well as some of its specific critical properties. The special case of a flow in the space-time of a non-rotating black hole, characterised by the Schwarzschild metric, has also been studied for comparison and the conclusions are compatible with what has been seen for the Kerr geometric case.

arXiv comment12 pages, 10 figures, mn2e.cls used

References in corpus (10)

• Viscous accretion discs around rotating black holes
• Geometrically Thin Disk Accreting Into a Black Hole
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• Acoustic horizons in axially symmetric relativistic accretion
• Dependence of General Relativistic Accretion on Black Hole Spin
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• Realizability of stationary spherically symmetric transonic accretion
• Evolution of transonicity in an accretion disc
• Behaviour of matter close to the event horizon

Cited by in corpus (18)

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• The role of flow geometry in influencing the stability criteria for low angular momentum axisymmetric black hole accretion
• Michel accretion of a polytropic fluid with adiabatic index gamma > 5/3: Global flows versus homoclinic orbits
• Fractal features in accretion discs
• Secular instability in quasi-viscous disc accretion
• On Spin Dependence of Relativistic Acoustic Geometry
• Critical properties of spherically symmetric accretion in a fractal medium
• Black Hole spin dependence of general relativistic multi-transonic accretion close to the horizon
• Quasi-viscous accretion flow -- I: Equilibrium conditions and asymptotic behaviour
• Axially Symmetric Accretion of Fractal Medium onto Rotating Black Holes and the emergence of the Acoustic Manifold
• Effective sound speed in relativistic accretion discs around Schwarzschild black holes
• Nonlinear variations in axisymmetric accretion
• Carter-Penrose diagrams for emergent spacetime in axisymmetrically accreting black hole systems
• On the efficiency of the Blandford-Znajek mechanism for low angular momentum relativistic accretion
• Effect of matter geometry on low angular momentum black hole accretion in the Kerr metric
• An Analytical Study on the Multi-critical Behaviour and Related Bifurcation Phenomena for Relativistic Black Hole Accretion
• Influence of matter geometry on shocked flows-I: Accretion in the Schwarzschild metric
• A Dynamical Systems Analysis of Axisymmetric Accretion in a Schwarzschild Black Hole