Influence of the geometric configuration of accretion flow on the black hole spin dependence of relativistic acoustic geometry

Linear perturbation of general relativistic accretion of low angular momentum hydrodynamic fluid onto a Kerr black hole leads to the formation of curved acoustic geometry embedded within the background flow. Characteristic features of such sonic geometry depend on the black hole spin. Such dependence can be probed by studying the correlation of the acoustic surface gravity $\kappa$ with the Kerr parameter $a$. The $\kappa - a$ relationship further gets influenced by the geometric configuration of the accretion flow structure. In this work, such influence has been studied for multitransonic shocked accretion where linear perturbation of general relativistic flow profile leads to the formation of two analogue black hole type horizons formed at the sonic points and one analogue white hole type horizon which is formed at the shock location producing divergent acoustic surface gravity. Dependence of the $\kappa - a$ relationship on the geometric configuration has also been studied for monotransonic accretion, over the entire span of the Kerr parameter including retrograde flow. For accreting astrophysical black holes, the present work thus investigates how the salient features of the embedded relativistic sonic geometry may be determined not only by the background space-time, but also by the flow configuration of the embedding matter.