The coupled hydrodynamic equations governing equatorial flows applicable to inviscid disc accretion in the Schwarzschild metric are solved analytically and numerically. Here, we concentrate on the transonic solutions, that represent physically allowed accretion on to black holes. A polytropic equation linking gas pressure and density is assumed, and solutions are obtained for different conditions, such as isothermal and adiabatic gas flows. The dependence of those solutions on the angular momentum is explored. Under certain conditions, when there exist multiple possible sonic points, the numerical simulation automatically zeros in to the unique transonic solution passing through one of the sonic points.
Kafatos, M., Yang, R. (1994) Transonic Inviscid Disc Flows in the Schwarzschild Metric – I, Monthly Notices of the Royal Astronomical Society, 268:925-937. doi: 10.1093/mnras/268.4.925
Royal Astronomical Society/Oxford University Press