Relativistic sonic geometry for isothermal accretion in the Schwarzschild metric

Abstract

In this work, we perform linear perturbation on general relativistic isothermal accretion onto a non-rotating astrophysical black hole to study the salient features of the corresponding emergent acoustic metric. For spherically symmetric accretion as well as for the axially symmetric matter flow for three different geometric configuration of matter, we perturb the velocity potential, the mass accretion rate, and the integral solution of the time independent part of the general relativistic Euler equation to obtain such acoustic geometry. We provide the procedure to locate the acoustic horizon and identify such horizon with the transonic surfaces of the accreting matter through the construction of the corresponding causal structures. We then discuss how one can compute the value of the acoustic surface gravity in terms of the accretion variable corresponding to the background flow solutions - i.e., stationary integral transonic accretion solutions for different matter geometries. We show that the salient features of the acoustic geometry is independent of the physical variable we perturb, but sensitively depends on the geometric configuration of the black hole accretion disc.

34 pages, 2 figures, completely rewritten, several new sections added

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Cited by in corpus (7)

• Linear perturbations of low angular momentum accretion flow in the Kerr metric and the corresponding emergent gravity phenomena
• Relativistic sonic geometry for isothermal accretion in the Kerr metric
• Influence of flow thickness on general relativistic low angular momentum accretion around spinning black holes
• Effective sound speed in relativistic accretion discs around Schwarzschild black holes
• Carter-Penrose diagrams for emergent spacetime in axisymmetrically accreting black hole systems
• Acoustic Analogue of Gravitational Wave
• Dynamical analogue spacetimes in non-relativistic flows