Acoustic geometry through perturbation of mass accretion rate: radial flow in static spacetimes

Ananda, Deepika B.; Bhattacharya, Sourav; Das, Tapas K.

doi:10.1007/s10714-015-1940-2

Cited by 29 publications

(37 citation statements)

References 34 publications

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“…Its surface gravity κ with respect to the Killing vector field k defined in Eq. (18), which will play an important role later, can be computed using Eqs. (11) and (13).…”

Section: Quasi-normal Oscillations From a Mode Analysismentioning

confidence: 99%

“…Here, σ denotes the decay rate, ω the frequency of oscillations, and Y m the standard spherical harmonics with angular momentum numbers m. Introducing this ansatz into Eq. (14) and using the diagonal parametrization (19) of the acoustic metric, one obtains the following equation:…”

Section: B Reduction To a Schrödinger-like Equationmentioning

confidence: 99%

“…[14], and for recent applications to accretion flows on black hole backgrounds, see Refs. [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…For the case of the Michel flow, for example, one can prove that acoustic perturbations outside the sonic horizon stay bounded, using standard energy conservation techniques [12,15,18]. In this article, we use this analogue black hole interpretation and show that, similar to the case in which a Schwarzschild black hole is perturbed, small perturbations of the Michel flow lead to quasi-normal acoustic oscillations characterized by complex frequencies s = σ + iω, where σ < 0 describes the decay rate and ω the frequency of oscillation.…”

Section: Introductionmentioning

confidence: 99%

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Quasinormal acoustic oscillations in the Michel flow

2015

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We study spherical and nonspherical linear acoustic perturbations of the Michel flow, which describes the steady radial accretion of a perfect fluid into a nonrotating black hole. The dynamics of such perturbations are governed by a scalar wave equation on an effective curved background geometry determined by the acoustic metric, which is constructed from the spacetime metric and the particle density and four-velocity of the fluid. For the problem under consideration in this article the acoustic metric has the same qualitative features as an asymptotically flat, static and spherically symmetric black hole, and thus it represents a natural astrophysical analogue black hole.As for the case of a scalar field propagating on a Schwarzschild background, we show that acoustic perturbations of the Michel flow exhibit quasi-normal oscillations. Based on a new numerical method for determining the solutions of the radial mode equation, we compute the associated frequencies and analyze their dependency on the mass of the black hole, the radius of the sonic horizon and the angular momentum number. Our results for the fundamental frequencies are compared to those obtained from an independent numerical Cauchy evolution, finding good agreement between the two approaches. When the radius of the sonic horizon is large compared to the event horizon radius, we find that the quasi-normal frequencies scale approximately like the surface gravity associated with the sonic horizon.

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“…Its surface gravity κ with respect to the Killing vector field k defined in Eq. (18), which will play an important role later, can be computed using Eqs. (11) and (13).…”

Section: Quasi-normal Oscillations From a Mode Analysismentioning

confidence: 99%

Section: B Reduction To a Schrödinger-like Equationmentioning

confidence: 99%

“…[14], and for recent applications to accretion flows on black hole backgrounds, see Refs. [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quasinormal acoustic oscillations in the Michel flow

2015

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“…In Moncrief's analysis, the acoustic wave in the accretion flow was shown to satisfy the Klein-Gordon-type wave equation. Some papers also apply the idea of the acoustic black holes to astrophysical phenomena [27][28][29][30][31][32][33][34]. In particular, Abraham et al [28] study the axially symmetric accretion flow onto a Kerr black hole and discuss a situation similar to the draining bathtub model with acoustic superradiance.…”

Section: Introductionmentioning

confidence: 99%

Analog rotating black holes in a magnetohydrodynamic inflow

Noda¹,

Nambu²,

Takahashi³

2017

Phys. Rev. D

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We present a model of the analog geometry in a magnetohydrodynamic (MHD) flow. For the MHD flow with magnetic pressure-dominated and gas pressure-dominated conditions, we obtain the magnetoacoustic metric for the fast MHD mode. For the slow MHD mode, on the other hand, the wave is governed by the advective-type equation without an isotropic dispersion term. Thus, the "distance" perpendicular to the wave propagation is not defined and the magnetoacoustic metric cannot be introduced. To investigate the properties of the magnetoacoustic geometry for the fast mode, we prepare a two-dimensional axisymmetric inflow and examine the behavior of magnetoacoustic rays which is a counterpart of the MHD waves in the eikonal limit. We find that the magnetoacoustic geometry is classified into three types depending on two parameters characterizing the background flow: analog spacetimes of rotating black holes, ultra spinning stars with ergoregions, and spinning stars without ergoregions. We address the effects of the magnetic pressure on the effective geometries.

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Quasi-normal acoustic oscillations in the transonic Bondi flow

Chaverra

Sarbach

2015

Gen Relativ Gravit

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In recent work, we analyzed the dynamics of spherical and nonspherical acoustic perturbations of the Michel flow, describing the steady radial accretion of a relativistic perfect fluid into a nonrotating black hole. We showed that such perturbations undergo quasi-normal oscillations and computed the corresponding complex frequencies as a function of the black hole mass M and the radius r_c of the sonic horizon. It was found that when r_c is much larger than the Schwarzschild radius r_H = 2GM/c^2 of the black hole, these frequencies scale like the surface gravity of the analogue black hole associated with the acoustic metric. In this work, we analyze the Newtonian limit of the Michel solution and its acoustic perturbations. In this limit, the flow outside the sonic horizon reduces to the transonic Bondi flow, and the acoustic metric reduces to the one introduced by Unruh in the context of experimental black hole evaporation. We show that for the transonic Bondi flow, Unruh's acoustic metric describes an analogue black hole and compute the associated quasi-normal frequencies. We prove that they do indeed scale like the surface gravity of the acoustic black hole, thus providing an explanation for our previous results in the relativistic setting.Comment: 18 pages, 3 figure

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Acoustic geometry through perturbation of mass accretion rate: radial flow in static spacetimes

Cited by 29 publications

References 34 publications

Quasinormal acoustic oscillations in the Michel flow

Quasinormal acoustic oscillations in the Michel flow

Analog rotating black holes in a magnetohydrodynamic inflow

Quasi-normal acoustic oscillations in the transonic Bondi flow

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