Newtonian analogue of corresponding space-time dynamics of rotating black holes: implication for black hole accretion (original) (raw)
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Based on the conserved Hamiltonian for a test particle, we have formulated a Newtonian analogue of Kerr spacetime in the ‘low energy limit of the test particle motion’ that, in principle, can be comprehensively used to describe general relativis- tic (GR) features of Kerr spacetime, however, with less accuracy for high spin. The derived potential, which has an explicit velocity dependence, contains the entire rela- tivistic features of corresponding spacetime including the frame dragging effect, unlike other prevailing pseudo-Newtonian potentials (PNPs) for the Kerr metric where such an effect is either totally missing or introduced in a ad hoc manner. The particle dynamics with this potential precisely reproduce the GR results within a maximum ∼ 10% deviation in energy for a particle orbiting circularly in the vicinity of a rapidly corotating black hole. GR epicyclic frequencies are also well reproduced with the po- tential, though with a relatively higher percentage of deviation. For counterrotating cases, the obtained potential replicate the GR results with precise accuracy. The Kerr- Newtonian potential also approximates the radius of marginally stable and marginally bound circular orbits with reasonable accuracy for a < 0.7. Importantly, the derived potential can imitate the experimentally tested GR effects like perihelion advance- ment and bending of light with reasonable accuracy. The formulated Kerr-Newtonian potential thus can be useful to study complex accreting plasma dynamics and its impli- cations around rotating BHs in the Newtonian framework, avoiding GR gas dynamical equations
Newtonian analogue of corresponding spacetime dynamics
2014
Based on the conserved Hamiltonian for a test particle, we have formulated a Newtonian analogue of Kerr spacetime in the 'low energy limit of the test particle motion' that, in principle, can be comprehensively used to describe general relativistic (GR) features of Kerr spacetime, however, with less accuracy for high spin. The derived potential, which has an explicit velocity dependence, contains the entire relativistic features of corresponding spacetime including the frame dragging effect, unlike other prevailing pseudo-Newtonian potentials (PNPs) for the Kerr metric where such an effect is either totally missing or introduced in a ad hoc manner. The particle dynamics with this potential precisely reproduce the GR results within a maximum ∼ 10% deviation in energy for a particle orbiting circularly in the vicinity of a rapidly corotating black hole. GR epicyclic frequencies are also well reproduced with the potential, though with a relatively higher percentage of deviation. For counterrotating cases, the obtained potential replicate the GR results with precise accuracy. The Kerr-Newtonian potential also approximates the radius of marginally stable and marginally bound circular orbits with reasonable accuracy for a < 0.7. Importantly, the derived potential can imitate the experimentally tested GR effects like perihelion advancement and bending of light with reasonable accuracy. The formulated Kerr-Newtonian potential thus can be useful to study complex accreting plasma dynamics and its implications around rotating BHs in the Newtonian framework, avoiding GR gas dynamical equations.
The Astrophysical Journal, 2007
We prescribe a pseudo-Newtonian vector potential for studying accretion disks around Kerr black holes. The potential is useful to study the inner properties of disk not confined to the equatorial plane where general relativistic effect is indispensable. Therefore, we incorporate the essential properties of the metric at the inner radii through the pseudo-Newtonian potential derived from the general Kerr spacetime. The potential, reproducing most of the salient features of the general-relativity, is valid for entire regime of Kerr parameter. It reproduces the last stable circular orbit exactly as that in the Kerr geometry. It also reproduces last bound orbit and energy at last stable circular orbit with a maximum error ∼ 7% and ∼ 15% respectively upto an orbital inclination 30 • .
Limitations of the pseudo-Newtonian approach in studying the accretion flow around a Kerr black hole
Physical Review D
We study the relativistic accretion flow in a generic stationary axisymmetric space-time and obtain an effective potential (Φ eff) that accurately mimics the general relativistic features of Kerr black hole having spin 0 ≤ a k < 1. Considering the accretion disc to be confined around the equatorial plane of a rotating black hole and using the relativistic equation of state, we examine the properties of the relativistic accretion flow and compare it with the same obtained form semi-relativistic as well as non-relativistic accretion flows. Towards this, we first investigate the transonic properties of the accretion flow around the rotating black hole where good agreement is observed for relativistic and semi-relativistic flows. Further, we study the non-linearities such as shock waves in accretion flow. Here also we find that the shock properties are in agreement for both relativistic and semirelativistic flows irrespective of the black hole spin (a k), although it deviates significantly for nonrelativistic flow. In fact, when the particular shocked solutions are compared for flows with identical outer boundary conditions, the positions of shock transition in relativistic and semi-relativistic flows agree well with deviation of 6 − 12% for 0 ≤ a k ≤ 0.99, but vast disagreement is observed for nonrelativistic flow. In addition, we compare the parameter space (in energy (E) and angular momentum (λ) plane) for shock to establish the fact that relativistic as well as semi-relativistic accretion flow dynamics do show close agreement irrespective of a k values, whereas non-relativistic flow fails to do so. With these findings, we point out that semi-relativistic flow including Φ eff satisfactorily mimics the relativistic accretion flows around Kerr black hole. Finally, we discuss the possible implications of this work in the context of dissipative advective accretion flow around Kerr black holes.
Monthly Notices of The Royal Astronomical Society, 2006
In this series of papers, we shall present a simplistic approach to the study of particle dynamics, fluid dynamics and numerical simulations of accretion flows and outflows around rotating black holes. We show that with a suitably modified effective potential of the central gravitating rotating object, one can carry out these studies very accurately. In this approach, one need not use the full general relativistic equations to obtain the salient features of the general relativistic flows provided the Kerr parameter remains within −1 ≤a≤ 0.8. We present the equatorial and the non-equatorial particle trajectories from our potential and compare salient properties in Kerr and in pseudo-Kerr geometries. Our potential naturally produces accurate results for motions around the Schwarzschild geometry when the black hole angular momentum is set to zero.
An analytic toy model for relativistic accretion in Kerr space-time
Monthly Notices of The Royal Astronomical Society, 2013
We present a relativistic model for the stationary axisymmetric accretion flow of a rotating cloud of non-interacting particles falling on to a Kerr black hole. Based on a ballistic approximation, streamlines are described analytically in terms of time-like geodesics, while a simple numerical scheme is introduced for calculating the density field. A novel approach is presented for describing all of the possible types of orbit by means of a single analytic expression. This model is a useful tool for highlighting purely relativistic signatures in the accretion flow dynamics coming from a strong gravitational field with frame dragging. In particular, we explore the coupling due to this between the spin of the black hole and the angular momentum of the infalling matter. Moreover, we demonstrate how this analytic solution maybe used for benchmarking general relativistic numerical hydrodynamics codes by comparing it against results of smoothed particle hydrodynamics simulations for a collapsar-like set-up. These simulations are performed first for a ballistic flow (with zero pressure) and then for a hydrodynamical one where we measure the effects of pressure gradients on the infall, thus exploring the extent of applicability of the ballistic approximation.
Highly relativistic circular orbits of spinning particle in the Kerr field
2013
The Mathisson-Papapetrou equations in Kerr's background are considered. The region of existence of highly relativistic planar circular orbits of a spinning particle in this background and dependence of the particle's Lorentz γ-factor on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle the corresponding orbits of a spinning particle are allowed in much wider space region. Some of these orbits show the significant attractive action of the spin-gravity coupling on a particle and others are caused by the significant repulsive action. Numerical estimates for electrons, protons and neutrinos in the gravitational field of black holes are presented.
An accurate Newtonian description of particle motion around a Schwarzschild black hole
Monthly Notices of The Royal Astronomical Society, 2013
A generalized Newtonian potential is derived from the geodesic motion of test particles in Schwarzschild space–time. This potential reproduces several relativistic features with higher accuracy than commonly used pseudo-Newtonian approaches. The new potential reproduces the exact location of the marginally stable, marginally bound and photon circular orbits, as well as the exact radial dependence of the binding energy and the angular momentum of these orbits. Moreover, it reproduces the orbital and epicyclic angular frequencies to better than 6 percent. In addition, the spatial projections of general trajectories coincide with their relativistic counterparts, while the time evolution of parabolic-like trajectories and the pericentre advance of elliptical-like trajectories are both reproduced exactly. We apply this approach to a standard thin accretion disc and find that the efficiency of energy extraction agrees to within 3 percent with the exact relativistic value, while the energy flux per unit area as a function of radius is reproduced everywhere to better than 7 percent. As a further astrophysical application we implement the new approach within a smoothed particle hydrodynamics code and study the tidal disruption of a main-sequence star by a supermassive black hole. The results obtained are in very good agreement with previous relativistic simulations of tidal disruptions in Schwarzschild space–time. The equations of motion derived from this potential can be implemented easily within existing Newtonian hydrodynamics codes with hardly any additional computational effort.
The Kerr spacetime: rotating black holes in general relativity
2009
Click here if your download doesn"t start automatically The Kerr Spacetime: Rotating Black Holes in General Relativity The Kerr Spacetime: Rotating Black Holes in General Relativity Rotating black holes, as described by the Kerr space-time, are the key to understanding the most violent and energetic phenomena in the Universe, from the core collapse of massive supernova explosions producing powerful bursts of gamma rays, to supermassive black hole engines that power quasars and other active galactic nuclei. This book is a unique, comprehensive overview of the Kerr space-time, with original contributions and historical accounts from researchers who have pioneered the theory and observation of black holes, and Roy Kerr's own description of his 1963 discovery. It covers all aspects of rotating black holes, from mathematical relativity to astrophysical applications and observations, and current theoretical frontiers. This book provides an excellent introduction and survey of the Kerr space-time for researchers and graduate students across the spectrum of observational and theoretical astrophysics, general relativity, and high-energy physics.
Particle dynamics near Kerr-MOG black hole
The European Physical Journal C
This paper explores the dynamics of both neutral and charged particles orbiting near a rotating black hole in scalar-tensor-vector gravity. We study the conditions for the particle to escape at the innermost stable circular orbit. We investigate the stability of orbits through the effective potential and Lyapunov exponent in the presence of a magnetic field. The effective force acting on particle is also discussed. We also study the center of mass energy of particle collision near the horizon of this black hole. Finally, we compare our results with the particle motion around Schwarzschild, Kerr and Schwarzschild-MOG black holes. It is concluded that the external magnetic field, spin parameter and dimensionless parameter of the theory have strong effects on the particle dynamics in modified gravity.