A black-hole accretion disc as an analogue gravity model

We formulate and solve the equations governing the transonic behaviour of a general relativistic black-hole accretion disc with non-zero advection velocity. We demonstrate that a relativistic Rankine-Hugoniot shock may form leading to the formation of accretion powered out flow. We show that the critical points of transonic discs generally do not coincide with the corresponding sonic points. The collection of such sonic points forms an axisymmetric hypersurface, generators of which are the acoustic null geodesics, i.e. the phonon trajectories. Such a surface is shown to be identical to an acoustic event horizon. The acoustic surface gravity and the corresponding analogue horizon temperature T-AH at the acoustic horizon are then computed in terms of fundamental accretion parameters. Physically, the analogue temperature is associated with the thermal phonon radiation, analogous to the Hawking radiation of the black-hole horizon. Thus, an axisymmetric black-hole accretion disc is established as a natural example of the classical analogue gravity model, for which two kinds of horizons exist simultaneously. We have shown that for some values of astrophysically relevant accretion parameters, the analogue temperature exceeds the corresponding Hawking temperature. We point out that acoustic white holes can also be generated for a multi-transonic black-hole accretion with a shock. Such a white hole, produced at the shock, is always flanked by two acoustic black holes generated at the inner and the outer sonic points. Finally, we discuss possible applications of our work to other astrophysical events which may exhibit analogue effects.