Carter-Penrose diagrams for emergent spacetime in axisymmetrically accreting black hole systems

TL;DR

This paper constructs Carter-Penrose diagrams for analogue spacetimes derived from axisymmetric accretion flows around Kerr black holes, revealing the relationship between sonic points, critical points, and acoustic horizons.

Contribution

It analyzes the causal structure of analogue spacetimes in accretion flows, showing how sonic and critical points relate to acoustic horizons in different flow configurations.

Findings

Critical points act as acoustic horizons in both flow types.

Sonic points coincide with critical points in conical flows.

In hydrostatic equilibrium flows, sonic points do not serve as acoustic horizons.

Abstract

For general relativistic, inviscid, axisymmetric flow around Kerr black hole one may choose different flow thickness. The stationary flow equations can be solved using methods of dynamical system to get transonic accretion flows , i.e, flow infalling in the blackhole that turns supersonic from subsonic with decreasing radial distance, or vice versa. This transonic flows are obtained by choosing the particular flow passing through critical points of phase portrait. For certain flow thickness like the one maintaining conical shape, the sonic point coincide with the critical point. But there are certain flows maintaining hydrostatic equilibrium, such as the one described by Novikov-Thorne, where the sonic point is not same as the critical point. We perturb the flow for both kind of flow and study the behaviour of linear perturbation which behaves like massless scalar field in some curved spacetime, known as, analogue space time. We draw the compactified causal structure, i.e, Penrose Carter diagram for both kind of analogue metric and prove that for both cases critical points are the acoustic horizons, whereas in the case where sonic points do not coincide with critical points, the sonic points are not the acoustic horizon, as one may expect from the definition of sound speed.