Generalized shock solutions for hydrodynamic black hole accretion

For the first time, all available pseudo-Schwarzschild potentials are exhaustively used to investigate the possibility of shock formation in hydrodynamic, inviscid, black hole accretion disks. It is shown that a significant region of parameter space spanned by important accretion parameters allows shock formation for flow in all potentials used in this work. This leads to the conclusion that the standing shocks are essential ingredients in accretion disks around nonrotating black holes in general. Using a complete general relativistic framework, equations governing multitransonic black hole accretion and wind are formulated and solved, and the condition for shock formation in such flows is also derived in the Schwarzschild metric. Shock solutions for accretion flow in various pseudopotentials are then compared with such general relativistic solutions to identify which potential is the best approximation of Schwarzschild spacetime as far as the question of shock formation in black hole accretion disks is concerned.