Standing shocks around black holes: An analytical study

We compute locations of sonic points and standing shock waves in a thin, axisymmetric, adiabatic flow around a Schwarzschild black hole. We use a completely 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 indicate 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.