  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.
