Effect of disc heights on acoustic surface gravity for accreting Kerr black holes

Abstract For axially symmetric accretion maintained in hydrostatic equilibrium along the vertical direction, we investigate how the characteristic features of the embedded acoustic geometry depend on the background Kerr metric, and how such dependence is governed by two different expressions for the geometrical configurations of the matter flow. We first obtain the location of the sonic points and stationary shock between the sonic points. We then perturb the flow to obtain the corresponding metric elements of the acoustic space-time. We compute the value of the acoustic surface gravity as a function of the spin angular momentum of the rotating black hole for the different flow thicknesses considered in the present work.