Relativistic sonic geometry for isothermal accretion in the Schwarzschild metric

Shaikh, Arif; Firdousi, Ivleena; Das, Tapas K.

doi:10.1088/1361-6382/aa7b19

Cited by 16 publications

(28 citation statements)

References 75 publications

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“…where H θ is the characteristic angular scale of the flow. Thus the continuity equation for vertically averaged axially symmetric accretion can be written as [15,17,65] ∂ t (ρv t −gH θ ) + ∂ r (ρv r −gH θ ) = 0 (13) whereg is the value of g, the determinant of the background metric g µν , on the equatorial plane. For Kerr metric g = − sin 2 θA 2 and thusg = −r 4 .…”

Section: Disc Structurementioning

confidence: 99%

“…In the majority of such works, characteristic features of the embedded sonic geometry have been obtained through perturbation of mass accretion rate in the astrophysical context. Shaikh et al [15] have studied the perturbation of isothermal accretion in a more general context, where a generalized formalism was presented to show how one can obtain the corresponding sonic geometry through the linear perturbation of the velocity potential, mass accretion rate as well as the relativistic Bernoulli's constant to manifest that there exist some general properties of the emergent gravity phenomena which are independent of the quantity that we linear perturb to obtain the spacetime geometry describing the emergence of the gravity like phenomena. In [15], the accretion dynamics was studied in the background Schwarzschild metric.…”

Section: Introductionmentioning

confidence: 99%

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Relativistic sonic geometry for isothermal accretion in the Kerr metric

Shaikh

2018

Class. Quantum Grav.

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We linearly perturb advective isothermal transonic accretion onto rotating astrophysical black holes to study the emergence of the relativistic acoustic spacetime and to investigate how the salient features of such spacetime get influenced by the spin angular momentum of the black hole. We have perturbed three different quantities -the velocity potential, the mass accretion rate and the relativistic Bernoulli's constant to show that the acoustic metric obtained for these three cases are same up to a conformal factor . By constructing the required causal structures, it has been demonstrated that the acoustic black holes are formed at the transonic points of the flow and acoustic white holes are formed at the shock location. The corresponding acoustic surface gravity has been computed in terms of the relevant accretion variables and the background metric elements. The linear stability analysis of the background stationary flow has been performed.

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Section: Disc Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Relativistic sonic geometry for isothermal accretion in the Kerr metric

Shaikh

2018

Class. Quantum Grav.

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“…where β for isothermal flow for different model is given is Table 1. The detailed derivation of acoustic metric for isothermal flow for vertical equilibrium model of ALP could be found in (Shaikh et al, 2017). The other models follows the same.…”

Section: Acoustic Metric For Isothermal Flowmentioning

confidence: 99%

“…Apart from the astrophysical point of view, accreting black hole systems have been studied from the perspective of emergent gravity phenomena (Das, 2004;Dasgupta et al, 2005;Abraham et al, 2006;Das et al, 2007;Pu et al, 2012;Bilic et al, 2014;Tarafdar and Das, 2015;Saha et al, 2016;Shaikh et al, 2017;Tarafdar and Das, 2018;Shaikh, 2018;Shaikh and Das, 2018) to understand how such systems can be perceived as an interesting example of classical analogue model naturally found in the universe. For such work also, the non-isomorphism between the critical and the sonic point may enhance the complexity involved with the solution scheme.…”

Section: Introductionmentioning

confidence: 99%

Effective sound speed in relativistic accretion discs around Schwarzschild black holes

Shaikh¹,

Maity²,

Nag³

et al. 2019

New Astronomy

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For low angular momentum axially symmetric accretion flow maintained in hydrostatic equilibrium along the vertical direction, the value of the Mach number at the critical points deviates from unity, resulting in the non-isomorphism of the critical and the sonic points. This introduces several undesirable complexities while analytically dealing with the stationary integral accretion solutions and the corresponding phase portraits. We propose that the introduction of an effective dynamical sound speed may resolve the issue in an elegant way. We linear perturb the full spacetime-dependent general relativistic Euler and the continuity equations governing the structure and the dynamics of accretion disc in vertical equilibrium around Schwarzschild black holes and identify the sonic metric embedded within the stationary background flow. Such metric describes the propagation of the linear acoustic perturbation inside the accretion flow. We construct the wave equation corresponding to that acoustic perturbation and find the speed of propagation of such perturbation. We finally show that the ordinary thermodynamic sound speed should be substituted by the speed of propagation of the linear acoustic wave which has been obtained through the dynamical perturbation. Such substitution will make the value of Mach number at the critical point to be equal to unity. Use of the aforementioned effective sound speed will lead to a modified stationary disc structure where the critical and the sonic points will be identical.

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“…Such an averaging is very common in accretion disc literature and is usually known as vertical averaging of the flow. Thus the continuity equation for vertically averaged axially symmetric accretion can be written as ( [74,75])…”

Section: Accretion Flow Geometrymentioning

confidence: 99%

Linear perturbations of low angular momentum accretion flow in the Kerr metric and the corresponding emergent gravity phenomena

Shaikh

Das

2018

Phys. Rev. D

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For certain geometric configuration of matter falling onto a rotating black hole, we develop a novel linear perturbation analysis scheme to perform the stability analysis of stationary integral accretion solutions corresponding to the steady state low angular momentum, inviscid, barotropic, irrotational, general relativistic accretion of hydrodynamic fluid. We demonstrate that such steady states remain stable under linear perturbation, and hence the stationary solutions are reliable to probe the black hole spacetime using the accretion phenomena.We report that a relativistic acoustic geometry emerges out as the consequence of such stability analysis procedure. We study various properties of that sonic geometry in detail. We construct the causal structures to establish the one to one correspondences of the sonic points with the acoustic black hole horizons, and the shock location with an acoustic white hole horizon. The influence of the spin of the rotating black holes on the emergence of such acoustic spacetime has been discussed.

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Relativistic sonic geometry for isothermal accretion in the Schwarzschild metric

Cited by 16 publications

References 75 publications

Relativistic sonic geometry for isothermal accretion in the Kerr metric

Relativistic sonic geometry for isothermal accretion in the Kerr metric

Effective sound speed in relativistic accretion discs around Schwarzschild black holes

Linear perturbations of low angular momentum accretion flow in the Kerr metric and the corresponding emergent gravity phenomena

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