Evolution of transonicity in an accretion disc

Abstract

For inviscid, rotational accretion flows driven by a general pseudo-Newtonian potential on to a Schwarzschild black hole, the only possible fixed points are saddle points and centre-type points. For the specific choice of the Newtonian potential, the flow has only two critical points, of which the outer one is a saddle point while the inner one is a centre-type point. A restrictive upper bound is imposed on the admissible range of values of the angular momentum of sub-Keplerian flows through a saddle point. These flows are very unstable to any deviation from a necessarily precise boundary condition. The difficulties against the physical realisability of a solution passing through the saddle point have been addressed through a temporal evolution of the flow, which gives a non-perturbative mechanism for selecting a transonic solution passing through the saddle point. An equation of motion for a real-time perturbation about the stationary flows reveals a very close correspondence with the metric of an acoustic black hole, which is also an indication of the primacy of transonicity.

18 pages

References in corpus (7)

• Black-Hole Accretion Disc as an Analogue Gravity Model
• Acoustic horizons in axially symmetric relativistic accretion
• Dependence of General Relativistic Accretion on Black Hole Spin
• Hydraulic Jump in One-dimensional Flow
• Critical properties and stability of stationary solutions in multi-transonic pseudo-Schwarzschild accretion
• The hydraulic jump as a white hole
• Behaviour of matter close to the event horizon

Cited by in corpus (14)

• Analogue Gravity
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• Axisymmetric black hole accretion in the Kerr metric as an autonomous dynamical system
• Perturbations on steady spherical accretion in Schwarzschild geometry
• Fractal features in accretion discs
• On Spin Dependence of Relativistic Acoustic Geometry
• 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
• Implications of nonlinearity for spherically symmetric accretion
• Nonlinear variations in axisymmetric accretion
• Carter-Penrose diagrams for emergent spacetime in axisymmetrically accreting black hole systems
• An Analytical Study on the Multi-critical Behaviour and Related Bifurcation Phenomena for Relativistic Black Hole Accretion