On Spin Dependence of Relativistic Acoustic Geometry

Abstract

This work makes the first ever attempt to understand the influence of the black hole background space-time in determining the fundamental properties of the embedded relativistic acoustic geometry. To accomplish such task, the role of the spin angular momentum of the astrophysical black hole (the Kerr parameter $a$ -- a representative feature of the background black hole metric) in estimating the value of the acoustic surface gravity (the representative feature of the corresponding analogue space time) has been investigated for axially symmetric inflow of hydrodynamic fluid onto a rotating black hole. Since almost all astrophysical black holes are supposed to posses some degree of intrinsic rotation, the influence of the Kerr parameter on classical analogue models is very important to understand. For certain values of the initial boundary conditions describing the aforementioned flow, more than one acoustic horizons, namely two black hole type and one white hole type, may form, where the surface gravity may become formally infinite at the acoustic white hole. The connection between the corresponding analogue Hawking temperature with astrophysically relevant observables associated with the spectral signature has been discussed.