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Cited article:

Relativistic sonic geometry for isothermal accretion in the Schwarzschild metric

Md Arif Shaikh, Ivleena Firdousi and Tapas Kumar Das
Classical and Quantum Gravity 34 (15) 155008 (2017)
https://doi.org/10.1088/1361-6382/aa7b19

Effect of an isotropic outflow from the Galactic Centre on the bow-shock evolution along the orbit

M. Zajaček, A. Eckart, V. Karas, et al.
Monthly Notices of the Royal Astronomical Society 455 (2) 1257 (2016)
https://doi.org/10.1093/mnras/stv2357

Generalized Shock Solutions for Hydrodynamic Black Hole Accretion

Tapas K. Das
The Astrophysical Journal 577 (2) 880 (2002)
https://doi.org/10.1086/342114