Standing shocks around black holes: An analytical study

We compute locations of sonic points and standing shock waves in a thin, ax isymmetric, adiabatic flow around a Schwarzschild black hole. We use a comp letely analytical method to achieve our goal. Our results are compared with those obtained numerically, and good agreement is seen. Our results prove the existence of shocks in centrifugal pressure-dominated flows. We indicat e how our results can be used to obtain spectral properties and frequencies of shock oscillations, which may be directly related to the quasi-periodic oscillations of hard X-rays.