The role of axisymmetric flow configuration in the estimation of the analogue surface gravity and related Hawking like temperature

TL;DR

This paper analytically examines how the flow configuration of an axially symmetric, dissipationless fluid influences the acoustic horizon, surface gravity, and Hawking-like temperature in a black hole analogue system.

Contribution

It provides an analytical study of the impact of flow geometry and background spacetime on acoustic surface gravity and Hawking temperature in black hole analogue models.

Findings

Acoustic horizon location depends on flow configuration.

Surface gravity varies with flow geometry and boundary conditions.

Analytical expressions for Hawking-like temperature derived.

Abstract

For axially symmetric flow of dissipationless inhomogeneous fluid onto a non rotating astrophysical black hole under the influence of a generalized pseudo-Schwarzschild gravitational potential, we investigate the influence of the background flow configuration on determining the salient features of the corresponding acoustic geometry. The acoustic horizon for the aforementioned flow structure has been located and the corresponding acoustic surface gravity $\kappa$ as well as the associated analogue Hawking temperature $T_{\rm AH}$ has been calculated {\it analytically}. The dependence of $\kappa$ on the flow geometry as well as on the nature of the back ground black hole space time (manifested through the nature of the pseudo-Schwarzschild potential used) has been discussed. Dependence of the value of $\kappa$ on various initial boundary conditions governing the dynamic and the thermodynamic properties of the background fluid flow has also been studied.