39 research outputs found

    Effective sound speed in relativistic accretion discs around rotating black holes

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    For axially symmetric accretion maintained in the hydrostatic equilibrium along the vertical direction in the Kerr metric, the radial Mach number does not become unity at the critical point. The sonic points are, thus, formed at a radial distance different from that where the critical points are formed. We propose that a modified dynamical sound speed can be defined through the linear perturbation of the full space-time dependent equations describing the aforementioned accretion flow structure. The linear stability analysis of such fluid equations leads to the formation of an wave equation which describes the propagation of linear acoustic perturbation. The speed of propagation of such perturbation can be used as the effective sound speed which makes the value of the Mach number to be unity when evaluated at the critical points. This allows the critical points to coalesce with the sonic points. We study how the spin angular momentum of the black hole (the Kerr parameter) influences the value of the effective sound speed

    Dependence of acoustic surface gravity on disc thickness for accreting astrophysical black holes

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    For axially symmetric accretion maintained in hydrostatic equilibrium along the vertical direction, we investigate how the characteristic features of the embedded acoustic geometry depends on the background Kerr metric, and how such dependence is governed by three different expressions of the thickness of the matter flow. We first obtain the location of the sonic points and stationary shock between the sonic points. We then linearly perturb the flow to obtain the corresponding metric elements of the acoustic space-time. We thus construct the causal structure to establish that the sonic points and the shocks are actually the analogue black hole type and white hole type horizons, respectively. We finally compute the value of the acoustic surface gravity as a function of the spin angular momentum of the rotating black hole for three different flow thicknesses considered in the present work. We find that for some flow models, the intrinsic acoustic geometry, although in principle may be extended up to the outer gravitational horizon of the astrophysical black hole, cannot be constructed beyond a certain truncation radius as imposed by the expressions of the thickness function of the corresponding flow.Comment: 22 pages, 9 figure

    Carter-Penrose diagrams for emergent spacetime in axisymmetrically accreting black hole systems

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    For general relativistic, inviscid, axisymmetric flow around Kerr black hole one may choose different flow thickness. The stationary flow equations can be solved using methods of dynamical system to get transonic accretion flows , i.e, flow infalling in the blackhole that turns supersonic from subsonic with decreasing radial distance, or vice versa. This transonic flows are obtained by choosing the particular flow passing through critical points of phase portrait. For certain flow thickness like the one maintaining conical shape, the sonic point coincide with the critical point. But there are certain flows maintaining hydrostatic equilibrium, such as the one described by Novikov-Thorne, where the sonic point is not same as the critical point. We perturb the flow for both kind of flow and study the behaviour of linear perturbation which behaves like massless scalar field in some curved spacetime, known as, analogue space time. We draw the compactified causal structure, i.e, Penrose Carter diagram for both kind of analogue metric and prove that for both cases critical points are the acoustic horizons, whereas in the case where sonic points do not coincide with critical points, the sonic points are not the acoustic horizon, as one may expect from the definition of sound speed.Comment: arXiv admin note: text overlap with arXiv:1811.0497
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