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In black hole evaporation process, the mass of the hole anti-correlates withthe Hawking temperature. This indicates that the smaller holes have highersurface gravity. For analogue Hawking effects, however, the acoustic surfacegravity is determined by the local values of the dynamical velocity of thestationary background fluid flow and the speed of propagation of thecharacteristic perturbation embedded in the background fluid, as well as bytheir space derivatives evaluated along the direction normal to the acoustichorizon, respectively. The mass of the analogue system - whether classical orquantum - does not directly contribute to extremise the value of the associatedacoustic surface gravity. For general relativistic axially symmetric backgroundfluid flow in the Schwarzschild metric, we show that the initial boundaryconditions describing such accretion influence the maximization scheme of theacoustic surface gravity and associated analogue temperature. Aforementionedbackground flow onto black holes can assume three distinct geometricconfigurations. Identical set of initial boundary conditions can lead toentirely different phase-space behavior of the stationary flow solutions, aswell as the salient features of the associated relativistic acoustic geometry.This implies that it is imperative to investigate how the measure of theacoustic surface gravity corresponding to the accreting black holes getsinfluenced by the geometric configuration of the inflow described by variousthermodynamic equations of state. Such investigation is useful to study theeffect of Einstenian gravity on the non-conventional classical features asobserved in Hawking like effect in a dispersive medium in the limit of a strongdispersion relation.

Dependence of acoustic surface gravity on geometric configuration of matter for axially symmetric background flows in the Schwarzschild metric ~